Can anyone explain by example?

Goal of OAuth is delegated authorization for which it defines a set of ways of obtaining a token. Once a token is obtained, that token could be used until expiry within the granted scope. I understand that we can just pass the token in the Authorization header to secure the APIs but how does ''all that happen in order to obtain the token'' fit into this context of API Connect?

For example, can anyone explain using a practical example of creating a REST proxy of swagger petstore API (given that the petstore API itself uses api-key or oauth in someway)

I've gone through the documentation but couldn't wrap my head around this yet.

Is OAuth provider same as Authorization server in Oauth spec?

How do all this fit together to create a functioning API spec in yaml?