Firstly, salad has both count and non-count usages:
salad [noun] [uncountable, countable]:
a mixture of raw vegetables such as lettuce, tomato and cucumber,
usually served with other food as part of a meal
[Oxford Advanced Learner's Dictionary]
count usages:
- [a] 'helpings / portions / complete meal' usage; compare 'two coffees' / 'three curries for table seven'.:
At a restaurant, two people might order, for instance, "two Caesar
salads." The noun is used countably when it refers to a single portion
served individually. Diners wouldn't be very likely to order "two
plates of Caesar salad" or somesuch.
[Glenfarclas; Word Reference Forum]
We had salads on Tuesday and Friday....
... So that's two salads already this week!
- [b] '[different] varieties of usage'; compare 'fifteen different ice creams are on offer':
Salad can be countable when referring to different sorts. "We've got
three salads: tomato, Greek and tuna."
[Hermione Golightly; Word Reference Forum]
noncount usage:
- We have some salad in the fridge. Compare 'we have some pork / chicken / rice / curry in the fridge.'
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The two statements given can be interchangeable (Master's comparison of the zero and indefinite articles), but 'I would like a salad' would be the usual choice if say 'Waldorf Salad' was offered as a complete dish and 'I would like [some] salad' when a side of salad was intended.