What is the difference between a review paper and a research paper? I have been working on a review paper. After publication, how will it add on my academic research profile? When I will apply for MS or PHD admission, will it count as publication?
A review paper is likely also known as a "survey paper", where you read (i.e. survey) related works in the field and then comment on them. Usually, a review paper should be able to contribute a small amount of knowledge in its own right to the field by providing a taxonomy of work.

Another type of paper that reviews extensively related work but isn't actually a review paper is a "systematic review paper" in which you usually ask a meta-question about the field.

If it appears in a refereed, peer-reviewed journal, then yes, it is a publication. In fact, if done well, these works can often have pretty high impact and can be cited very frequently. However, as already noted, since they don't usually involve substantial original research they need to be augmented with traditional research papers. If a graduate student has only survey papers or systematic review papers, I'd wonder as a search committee reviewer if this student did nothing but read related work rather than working on research.

With respect to MS or PhD applications, I'd think that the fact that you have a publication at all is already a bonus point for you. Most students who apply to these programs don't have publications.