The first two, unlike a research article, don't go through the process of double blind peer review, and are not seen as valuable scientific contribution, but, a case report may be very valuabe for an organization who asked for your assesment (for example the quality of a school) . a short communication can mean many things, for example, a short PR piece on your project/research/article
It depends on the outlet you are writing for - some journals include case reports, short communications, and research articles all within their peer review process, whereas others do not. It might help to check with the specific journal you are targeting first. If you are asking for a basic description of the difference, I can speak from a nursing journal standpoint - a case report describes a particularly challenging or unique case through an evidence-based lens with recommendations for future practice. A short communication may be commentary on a previously published article, a brief literature review with an editorial voice, or a short description of a program or intervention you have developed. Then, a research article would be a description of a study you conducted from beginning to end, grounded in current theory and evidence with a discussion of the implications and limitations of this work. Hope this helps!
A Case Report describes a particular case regarding anyone or anything unusual that has happened. It comes with preventive measures to undo those events in case of a patient.
A research article (Longer) gives full authenticity to their authors of what they have done for their particular study of interest. It comes with some new aspects to the previous work or give light on new works related to the study of interest.
A short communication (Shorter) is somewhat similar to the article but this is based on the review of many literature on the study of interest. It comes with a significant observation but without any explanation. Hope you like it.
Case report is the observations on new things or animal model it may be interaction/ succession of animal etc. but in case short communication it may be an abstract while Research article is an peer reveiwed publication containing authenic observations