They have very different meanings. Analogy is about transfering information, and similitude is about have something the same or nearly the same.
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Analogy (from Greek "??a????a" - analogia, "proportion"[1][2]) is a cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction