Pivotal GemFire is a product available for sale or subscription from Pivotal and Apache Geode, on the other hand, is the open source version of Pivotal GemFire. That said, Pivotal provides enterprise support for Pivotal GemFire but not for Apache Geode, which is only offered through the community.
That said, the source code between Apache Geode and Pivotal GemFire is shared but the binaries might be different, basically because they will typically be released at different points in time, Pivotal GemFire releases will have a much higher level of testing (meaning that some of the bugs within Apache Geode will also exist in Pivotal GemFire, some won't).
Pivotal Cloud Cache (PCC) is a high-performance, highly available caching layer for Pivotal Cloud Foundry (PCF) backed by GemFire, but I believe only a subset of GemFire functionalities are currently available.
Hope this helps, you can open a ticket with Pivotal Support for more detailed information.