Rest API or Supabase API

For connecting to Supabase what are the benefits of using the Rest API vs Supabase API? Why?
For Auth, What are the benefits to using the Supabase, vs the WeWeb APIs? Why?
I have managed to connect using the Supabase API but have not done so with the Rest APi. It appears o want different info. Excuse my ignorance as I am a newbie.

Also, can I connect directly to PostgreSQL with the Rest API?

It might be because the plugin has in its depencies supabase-js i guess