A research paper is one where you have a specific topic and you find information to support that topic. You may research the use of characterization in Frankenstein, the themes, or the use of symbolism. You will paraphrase the information you find, or you may quote directly from a source. All information you use from other sources must be cited and listed in a bibliography.
A critical analysis paper is one where you act as a reviewer of a piece of literature, analyzing each part of the work. It is a critical overview of the whole work. In this type of paper, you would analyze each part of Frankenstein. Depending upon your assignment, you may research what other critics say about the book to support your opinion.
I have included links below to help you in writing a research paper, and if you have specific questions regarding any of it, please ask.
A critical analysis paper and a research paper are different sorts of academic work although it is possible they may have some elements that overlap. First consider what goes into a critical analysis paper. In critical analysis, the academic (you) examines the text for literary elements of structure, theme, characters; literary techniques of imagery, symbolism, and other literary techniques like metonymy, synecdoche, personification, allusion etc. The academic doesn't need to know anything about the author or the time period or the literary period in order to perform a critical analysis; though it is true that this knowledge may be useful and helpful. In conjunction with this, a critical analysis may have a section on background or critical analysis by other academics; it is in this element that a critical analysis paper may overlap with a research paper.
A literary research paper requires research into factual information. While a research paper may also have a section that includes original analysis, most of the paper will cover the author's personal, educational, and writing background; the literary period in which the author wrote; the historical context surrounding the time in which the author wrote. A research paper must also include a section discussing what previous critical opinion said, in other words, what previous critics had to say about the work. A research paper will also say something about how the work being researched fits in with the author's whole body of writing. To summarize, a critical analysis is mostly your original analysis though there may perhaps be some background material included, whereas a research paper is a study of the author's life, historic times, literary period and the opinions of previous critics though it may perhaps have some original analysis.