It's almost equal phrases on practice.
But if to go into the theory, then "на русском (языке)" mean just using russian language in speech. But to do smth "по-русски" (without "й" in the endling, it's adverb, but not adjective), for example, to speak, mean make it in russian style, by russian way, of course, it include speaking in russian language by default.
PS: I often say to foreigners that "i don't speak english language, i speak russian with english words". This sentence can say in russian something like: "Я не говорю по-английски, я говорю на аглийском (языке) по-русски".