I think the author rushed at the end and didn't explain these details with clarity.
The both modes have different databooks entry, with Naruto only listed user of Six Path Sage Mode. It's also stated that Hagoromo have given this power for first time.
But when Madara sees the cloaked Naruto, he says Naruto has awakened Six Path Senjutsu.
Madara and Obito awakened Six Path Senjutsu by sealing Juubi inside them, and I think Naruto awakened Six Path Senjutsu because he got a portion of chakra of every tailed beast, but it's not a sole factor. I mean I don't think it is possible for any random ninja to get Six Path Senjutsu by merely getting the chakra of every every tailed beast.
So, what is the difference between these two modes? Since the Manga has not make any clear distinction between the two.