Mostly Ivy League Schools have the BS/BA Senior Thesis. For psychology majors, normally you enroll in a Independent Study course your Junior and Senior year and gain experience in research as part of a team being a research assistant for doctoral level students and faculty. I believe the concept for Senior Thesis is based on Private Ivy League School curriculum and generally is not a research project where you collect data. I believe it is more of a intellectual endeavor or creative project. The FedEx founder, Fred Smith did his Senior Thesis or paper on the concept of overnight delivery or overnight mail. He was actually mocked by faculty at Yale claiming it was poorly thought through and it would never be a practical concept and he received a C grade. I wonder what they would have thought about our current system of emailing legal documents!
Typically a 'senior' thesis is known as an 'honors' thesis in most undergraduate institutions. I would call your work an independent project and detail what you did and learned from it - but would not try to pass it off as an honors thesis, as that usually implies different things (e.g., at some universities you can only graduate with honors if you did an honors thesis).
"I wrote my proposal in my research design course and this past semester conducted and finished the manuscript for credit with my professor."
Also -- it's unclear to me whether you just wrote a proposal for a study, or whether you actually carried out the study, analyzed the results, and wrote it up. If the latter, it will have more weight and be something you should mention in applications/interviews (otherwise, if the former, I would consider it more like any other final paper we do in undergraduate courses at universities... which I never mentioned in applications).
Finally, I went to Harvard undergrad. and we call ours an 'honors' thesis and not everyone has to do one.... so the Ivy league specific thing, isn't as accurate anymore (i.e., as another poster said, it's not just an ivy league thing... unless you're differentiating senior vs. an honors thesis). It depends the field on whether an undergraduate honors thesis is experimental research or not. My friends who majored in history, for example, would complete a thesis that was essentially a big literature review whereas those in biology, chemistry, psychology, etc. had to conduct a study --- all where considered an honors thesis (requirements were defined by the specific department).
Anyway, although I am advising you not to necessarily call this project an honors/senior thesis - I would encourage you (whether you publish it or not) to mention it in your application as an undergraduate research project and to detail it (and be ready to talk about it during interviews). [On your cv you can do a poster, or manuscript in preparation until you get it published... and if this is a study you designed and conducted, analyzed and wrote up (which is the way I read your post originally) it is a notable accomplishment and something you should mention either in your personal statement or somewhere in a statement on research experience; some schools will even ask for writing samples and you can submit it
🙂].