I agree with Bruce, in noun form, they are synonyms. However, 'advocate' can also be a verb and then it would be used in a different way (as xarmania explains).

Many sources write that they are synonyms, but I use the words somewhat differently. If I am a proponent of something then I may advocate for it. The word proponent expresses my stance (in favor) whereas advocate expresses what I do because of my stance.

They are synonyms.