I’m interested in submitting a paper for a Student Paper Award at a conference. I’m wondering whether I can submit the same paper to a peer reviewed journal after the conference ends. Does the answer change depending on whether I win the student paper award or not? I’m a student in STEM in the US.
To give a perspective from the field of chemistry/materials science:
Conference contributions usually are posters and talks. Posters are usually presented by PhD students or younger researchers and often show results that are not mature enough to land a paper in a journal. Talks are usually presented by more experienced researchers or advanced PhD students and often reiterate the contents of a single or several (possibly) published journal papers. So in both cases, having both a journal paper and conference contributions from the same results is perfectly within the norm, and also simultaneous submission of a journal article and a conference contribution is no problem.
Note however that proper conference papers - although they exist sometimes - are rare in these cases. In my experience they are usually filled with some less important data that is of decent quality, but insufficient for a journal paper.
In addition to @Snijderfey's excellent answer, you might consult the website for the specific conference you are considering submitting to. Some directly address this issue. Here's an example from a conference I am attending:
Abstracts will not be indexed in MEDLINE, enabling authors to submit their best work that is destined for future journal publication. Contributions may also consist of abstracts based on work published in peer-reviewed journals in the last year (i.e., publication after March 2019); however, works published as proceedings for other conferences will not be accepted. Citation of the previous work is required.
You will typically find these statements in the instructions for authors or call for abstracts section. This answer assumes that you have selected the conference with the assistance of your mentor.
In general, simultaneous submission to different publishing venues is strongly frowned upon. After the conference ends, assuming the paper was accepted, is a different matter.
The outcome would depend on the policies of the journal, but most journals might decline to publish something that has already been "published" in another venue, other than as a preprint. But, in some fields, conferences aren't publishing venues and are rather more informal that in others. But it seems doubtful that a non publishing conference would be giving "best student paper" awards.
If you have a journal in mind, you could ask its editor for guidance. It might actually depend on what happens to the conference paper after the conference itself. Some are published by the sponsor of the conference in a proceedings.
Note that in some STEM fields (CS, especially), conference papers are considered very important. In that case, there would be little need to also seek journal publication.
If the paper is rejected, you are free, of course.
Also be careful about any license you give for a conference paper. If you give a permissive license then a publisher might be less likely to want your paper, since the copyright you give them is already limited. Many would prefer to get "all rights", or nearly all.
But to take the topline question literally, yes, you could possibly submit it. But at some point you will probably have to reveal its history and will have to mention the conference. I think it better to ask first. An editor who spends effort on something that they "can't" publish will be unhappy.
Here is a pure math perspective.
It is not possible to publish the same paper in conference proceedings and a normal journal. However, it is reasonably common to have a condensed version (an "extended abstract") in a conference and still publish the full version (which is expected to have significantly more material) subsequently in a journal. Typically most of the proofs will be omitted from the condensed version (and hence a conference publication which does not ultimately produce a journal publication is essentially worthless, as the refereeing process for conferences does not verify correctness).
If attempting to do this, it is sensible to ask the journal you're thinking of submitting to about their policy before submitting to the conference.