Usage of Identity Federation

There are some confuses of Identity Federation(OpenIDConnect). If i am going to integrate a Identity Provider then no need to write login logic & source code, no need to create user table and manange the user info, is it right ? and the identity provider will privde those functions. My resource API will be protected as resouce server in my side ?

But i found lots of APPs provider some of the third part login mechenism such as google, twitter, facebook, They just fetch a ID Token from IDP and create a new user in the Identity System of their owns, So, Dose it being misused of the concepts of Identity Federation here ?

B.T.W, Mostly, Seems, It is not accepted in mind if login through the third part identity system if a company create some of Apps, Company wannt the identtiy system of their own.. So , Is there any way to simplely make me own as a IdP? Does Amazon has a similar service?

Thx All~