APC is Ariba's cloud-based catalog solution which allows buying organizations to extend the value of there ERP or existing Procurement tools (SRM, Oracle iProcure, existing On-Prem) by giving users a easy-to-use catalog interface and catalog management capabilities.
Ariba punchout and "punchout" is a generic term for a process where a buyer leaves ("punches out" from) their company's eProcurement system to access a supplier's web-based catalog to do the shopping before returning the shopping cart information back to the eProcurement system for completion of the PO process.
In one sense, APC is also a "punchout" solution but the idea is the buying organization manages there own content (available catalog items, relevance, pricing, etc.) as opposed to having a supplier manage it.
Thanks for the response! I was thinking there is an Ariba application called "Ariba Punchout". Apparently it is just a general term.