Claims are specific attributes about a user. Wiki defines it as "A claim is a statement that one subject, such as a person or organization, makes about itself or another subject. For example, the statement can be about a name, group, buying preference, ethnicity, privilege, association or capability. ".
A scope is an indication by the client that it wants to access some resource, your server may allow or reject this. Oracle - Oauth Scopes
To provide an example, in your application your user may have a name, email and company name - these are your claims. That client may request access to your Admin controller of your Web API, this would be a scope. In an SSO environment, it could be some other application in its own right such as another API.
Google use scopes to control access to data transfer / analytics / ads APIs
Google Oauth Docs