Is a philosophy and quote the same thing?

Not necessarily. A philosophy is a general system of thought that explains or ties together general ideas of a topic. There is a philosophy of science, for example. There are philosophies that deal with the purpose of existence, the nature of knowledge, etc. A quote is simply a documented statement made by someone. Quotes can be about anything, serious or silly. A quote might have something to do with a philosophy, but it doesn't have to. Most serious philosophies can't be summarized in a single quote.

Sometimes a person might say something like: "My philosophy on that subject is that we should amend the Constitution." Probably, it would be better to refer to such a statement as an opinion and not a philosophy.