Oauth supports different Grant Types for the differing communications you're asking about.
Here is an example in a PHP library , of a different grant type or two:
Client Credentials Grant Type Trusted Clients and UnTrusted Clients
Client Credentials grant type is used when the client is requesting access to protected resources under its control (i.e. there is no third party).
# using HTTP Basic Authentication
$ curl -u TestClient:TestSecret https://api.mysite.com/token -d 'grant_type=client_credentials'
# using POST Body
$ curl https://api.mysite.com/token -d 'grant_type=client_credentials&client_id=TestClient&client_secret=TestSecret'
You'd get back an access token (like your cookie) and use that on all subsequent calls.
Implicit Grant Type
Source : http://bshaffer.github.io/oauth2-server-php-docs/grant-types/client-credentials/