Claims Based Authentication
Claims are a set of information stored in a key – value pair form. Claims are used to store information about user like full name, phone number, email address…. and the most important thing is that you can use claims as a replacement of roles, that you can transfer the roles to be a claim for a user.
The most important benefit from claims is that you can let a third party authenticate users, and the third party will retrieve to you if this user is authenticated or not and also what claims are for this user.
Token Based Authentication
Token store a set of data in (local/session storage or cookies), these could be stored in server or client side, the token itself is represented in hash of the cookie or session.
In token based authentication, when a request comes, it should have the token with it, the server first will authenticate the attached token with the request, then it will search for the associated cookie for it and bring the information needed from that cookie.