ABAC is a generic term and access control model much like RBAC is. Both are defined and formalized by NIST. In their latest publication, NIST consider ABAC as the next evolution in access control.
CBAC on the other is not a model. It's vendor-specific, in this case Cisco. You can see CBAC as a specialization of ABAC.
I've written most of the ABAC Wikipedia page so I'll naturally recommend you check it out. There are implementations of ABAC out there (e.g. Axiomatics which is where I work) which you can use to define fine-grained access control on APIs, databases, and more.
Lastly, there is a standard that implements ABAC: XACML or extensible access control markup language