"Statement of purpose" vs "Research proposal" in the context of graduate studies? After consulting google, what I am able to understand is that a statement of purpose is a document that is used when applying for graduate studies and it mentions the aptitude and motivation for research in a particular field
Is my understanding correct? If yes, then what is a research proposal?
Yes, your understanding is correct. While the CV lists past accomplishments, your SoP is a statement about your future goals, both for graduate study and thereafter. It need not, in general, be specific about a research topic, just a fairly narrow area.
A Research Proposal, on the other hand, is a specific outline of a research project that you suggest you would want to carry out. An advisor might accept such a proposal unchanged, but might also want to modify it, perhaps drastically. But it shows that you have given serious thought to at least one problem and have done some background on it.
A really complete research proposal would include a statement of the problem to be studied and questions to be answered, a preliminary suggestion of how the question will be attacked, and even suggestions about sources for any needed funding.