re: "...the difference between current and power."
"current" is measured in (A)mps & "power" is measured in (W)atts.
Power (in Watts) = V * A
Therefore, "the difference" is that current is a factor of power.
Note also, electric "current" is the flow of energy (via electric charge) over time (e.g.: an Ampère = 1 Coulomb/Second) = the current that one volt can send through one ohm of resistance in 1 Second.

re: "So it seems that wattage is the important thing to understand in many cases."
Appliances are rated in Watts (which is power) so that you can compare appliances to determine which will cost you the least to operate (e.g. refrigerators). Power ratings can also be used to determine which device may operate more vigorously than another device (e.g. blenders)--once again for potential buyer comparison purposes.

re: "A power supply is (from what I understand) usually given with a (max) voltage and a (max) current. Why is the wattage not given here?"
Many power supplies are advertised by the max wattage (e.g. a computer switching power supply). In other situations, the manufacturer &/or the seller may not include wattage information because they have no requirement to do so (e.g. som exported foreign products) and if they did provide it, then their product/s may not be as attractive to potential customers as other available products--therefore it is left out by the seller with the hope that some unsuspecting customer (hopefully with low initial power needs) will buy their product/s.

re: LED Wattage "...Why isn't the wattage listed?"
When you buy LEDs from a reputable source, datasheets will be available for their products. Those datasheets will indicate current consumption at various voltages levels. With that information, you can calculate the power (Watts) that will be consumed. When you buy LEDs online or from bulk bins at many electronics parts stores, they often do not provide datasheets for such parts. Sometimes you can get the manufacture & part numbers from such sellers & then look up the datasheets online--but that isn't always possible. Some times, technical information is not provided because the seller doesn't have such information (they may have bought their inventory at a bankruptcy auction, for example) or they are too lazy to make such information available for their potential customers.

re: "...the difference between current and power."
"current" is measured in (A)mps & "power" is measured in (W)atts.
Power (in Watts) = V * A
Therefore, "the difference" is that current is a factor of power.
Note also, electric "current" is the flow of energy (via electric charge) over time (e.g.: an Ampère = 1 Coulomb/Second) = the current that one volt can send through one ohm of resistance in 1 Second.

re: "So it seems that wattage is the important thing to understand in many cases."
Appliances are rated in Watts (which is power) so that you can compare appliances to determine which will cost you the least to operate (e.g. refrigerators). Power ratings can also be used to determine which device may operate more vigorously than another device (e.g. blenders)--once again for potential buyer comparison purposes.

re: "A power supply is (from what I understand) usually given with a (max) voltage and a (max) current. Why is the wattage not given here?"
Many power supplies are advertised by the max wattage (e.g. a computer switching power supply). In other situations, the manufacturer &/or the seller may not include wattage information because they have no requirement to do so (e.g. some exported foreign products) and if they did provide it, then their product/s may not be as attractive to potential customers as other available products--therefore it is left out by the seller with the hope that some unsuspecting customer (hopefully with low initial power needs) will buy their product/s.

re: LED Wattage "...Why isn't the wattage listed?"
When you buy LEDs from a reputable source, datasheets will be available for their products. Those datasheets will indicate current consumption at various voltages levels. With that information, you can calculate the power (Watts) that will be consumed. When you buy LEDs online or from bulk bins at many electronics parts stores, they often do not provide datasheets for such parts. Sometimes you can get the manufacture & part numbers from such sellers & then look up the datasheets online--but that isn't always possible. Some times, technical information is not provided because the seller doesn't have such information (they may have bought their inventory at a bankruptcy auction, for example) or they are too lazy to make such information available for their potential customers.

re: "...the difference between current and power."
"current" is measured in (A)mps & "power" is measured in (W)atts.
Power (in Watts) = V * A
Therefore, "the difference" is that current is a factor of power.
Note also, electric "current" is the flow of energy (via electric charge) over time (e.g.: an Ampère = 1 Coulomb/Second) = the current that one volt can send through one ohm of resistance in 1 Second.

re: "So it seems that wattage is the important thing to understand in many cases."
Appliances are rated in Watts (which is power) so that you can compare appliances to determine which will cost you the least to operate (e.g. refrigerators). Power ratings can also be used to determine which device may operate more vigorously than another device (e.g. blenders)--once again for potential buyer comparison purposes.

re: "A power supply is (from what I understand) usually given with a (max) voltage and a (max) current. Why is the wattage not given here?"
Many power supplies are advertised by the max wattage (e.g. a computer switching power supply). In other situations, the manufacturer &/or the seller may not include wattage information because they have no requirement to do so (exported foreign products) and if they did provide it, then their product/s may not be as attractive to potential customers as other available products--therefore it is left out by the seller with the hope that some unsuspecting customer (hopefully with low initial power needs) will buy their product.

re: LED Wattage "...Why isn't the wattage listed?"
When you buy LEDs from a reputable source, datasheets will be available for their products. Those datasheets will indicate current consumption at various voltages levels. With that information, you can calculate the power that will be consumed. When you buy lots of LEDs online or from bulk bins at many electronics parts stores, they often do not provide datasheets for the parts. Sometimes you can get the manufacture & model numbers from such sources & then look up the datasheet, but that isn't always possible. In such cases, technical information is not provided because the seller doesn't have such information (they may have bought their inventory at a bankruptcy auction, for example) or they are too lazy to make such information available for their potential customers.

re: "...the difference between current and power."
"current" is measured in (A)mps & "power" is measured in (W)atts.
Power (in Watts) = V * A
Therefore, "the difference" is that current is a factor of power.
Note also, electric "current" is the flow of energy (via electric charge) over time (e.g.: an Ampère = 1 Coulomb/Second) = the current that one volt can send through one ohm of resistance in 1 Second.

re: "So it seems that wattage is the important thing to understand in many cases."
Appliances are rated in Watts (which is power) so that you can compare appliances to determine which will cost you the least to operate (e.g. refrigerators). Power ratings can also be used to determine which device may operate more vigorously than another device (e.g. blenders)--once again for potential buyer comparison purposes.

re: "A power supply is (from what I understand) usually given with a (max) voltage and a (max) current. Why is the wattage not given here?"
Many power supplies are advertised by the max wattage (e.g. a computer switching power supply). In other situations, the manufacturer &/or the seller may not include wattage information because they have no requirement to do so (e.g. som exported foreign products) and if they did provide it, then their product/s may not be as attractive to potential customers as other available products--therefore it is left out by the seller with the hope that some unsuspecting customer (hopefully with low initial power needs) will buy their product/s.

re: LED Wattage "...Why isn't the wattage listed?"
When you buy LEDs from a reputable source, datasheets will be available for their products. Those datasheets will indicate current consumption at various voltages levels. With that information, you can calculate the power (Watts) that will be consumed. When you buy LEDs online or from bulk bins at many electronics parts stores, they often do not provide datasheets for such parts. Sometimes you can get the manufacture & part numbers from such sellers & then look up the datasheets online--but that isn't always possible. Some times, technical information is not provided because the seller doesn't have such information (they may have bought their inventory at a bankruptcy auction, for example) or they are too lazy to make such information available for their potential customers.