What is the differentiation between banking as a service and an issuer processor?

Technically no. It's a little bit broader. The processor or an issuer can actually be even something like a bank itself. So the banking as a service, in general, is an abstraction layer over an existing bank that includes technology software, APIs, and usually sits on top of a bank core. There's a few cores out there, right? Jack Henry, Fiserv, FIS. 

Some banks have tried to build it. A lot of technology companies are building it, but it's a little bit different than a processor or as an issuer. A banking-as-a-service solution can be a processor or can be an issuer, but it's a larger set, I would say.