If it didn't matter, then there would be no need to distinguish between the two.
Sure there is. To cover their bases against people just... like... you. "But they didn't say 'the People', they said 'the people', and they didn't say 'State and Federal and Homerule City', so they must have meant just Federal even though they never drew a distinction as to who may not do the 'infringing' despite a 'Supreme Law of the Land' clause".
Shall not be infringed. By anyone. For any reason. The only reasonable way to remove access to this Right is to deprive them of their freedom via incarceration for an actual crime. Not this made up a priori garbage.