What matters is the content of the file, not the extension. Both of those extensions imply that some sort of diff utility (diff, git diff, git format-patch, svn diff) produced the output.
Many diff utilities produce output which can be applied by the patch command. You will frequently need to use the -d and -p options to patch in order to get the paths matched up right (strip prefix, name target directory). If you see one of those extensions on a file distributed online, it’s almost certainly an indication it’s compatible with patch.
Git’s diff output is compatible with patch, but I believe svn’s is not. Of course, plain patches generated by git diff are probably best applied by git apply, and patches generated by git format-patch are designed for use with git-am.