Completed work consists of work where you've gone through all the steps of formulating your research question, applying a methodology, and generating and analyzing results. Incomplete work is where you're still in the phase of applying your methodology, or you haven't fully analyzed the results to figure out what they mean. A paper or poster on incomplete work might focus on the methodology or preliminary results, but it doesn't fully answer the questions posed when the work began.

There's definitely a judgement call when you can consider work "completed". Oftentimes, the answers to research questions lead to more questions, creating a line of related work that's never really "finished". In this case, you'll need to compartmentalize your results into digestible chunks that can be considered "completed". Describing future work planned on a project doesn't mean that a work is incomplete.

For a work to be "completed", it doesn't necessarily have to have been written up already. That said, you'll probably have to write up the work before submitting anyway. You almost certainly shouldn't be submitting the same work to a journal and a conference. You could try to submit "incomplete" work to the conference, since it's a somewhat fuzzy line, but don't be surprised if you get a rejection if all you've got is the methodology and no results at all.