Vercel, the company/service, used to be called Now. With any renaming comes some consistency challenges, even at the level of software.
The naming of the file for configuring your project used to be now.json. It
is now vercel.json.
For backwards compatibility reasons, you can still use either. You cannot and should not have both though.
If you're working with an existing project that uses now.json. It is fine to
continue with that naming. It may eliminate some future confusion if you are to
rename it to vercel.json. If you're starting a new project, I'd recommend
using vercel.json. All the documentation you'll read uses this newer naming
convention.