Usually name your price is points/cash and offer to adopt can be points, cash, art, adoptables, customs, etc...
But basically they mean the same thing :3 Hope that helped, I'm bad at explaining.
I think that with 'Name your price', the name pretty much explains it. You offer either points or money, depending on what the artist wants, while with Offer to Adopt, you can offer more things, like art, literature and points. :3