It is not UCaaS
Unified communications as a service is a finished internal collaboration product, defined by TechTarget as "a cloud delivery model for communications and collaboration services, including telephony, messaging, video conferencing and mobility" and elsewhere as "a ready-made platform where clients access different services, such as phone, video calling and call recording."[16][2] The everyday framing is that UCaaS improves how employees communicate with each other rather than supplying tools to customers.[15] Plenty of companies run both, using UCaaS for staff phones and CPaaS for the notifications their software sends out.
It is not CCaaS
Contact center as a service is the customer support product. TechTarget defines it as "a cloud delivery model for contact center infrastructure and apps, such as interactive voice response systems, teletypewriter (TTY)/telecommunications device for the deaf (TDD) communications, and workforce management," bought as a cloud subscription to support customers and prospects rather than internal staff.[16][15] Many CCaaS platforms run on CPaaS underneath, which is why both categories keep turning up in one vendor's catalog.
It is not a phone system
A CPaaS contract gives you numbers and call control rather than a directory of extensions with voicemail attached. You can build those on top of call automation APIs, and some companies do, but nothing in the API bundle configures a dial plan for you.[3]
It is not NIST platform as a service
The name echoes the NIST cloud taxonomy, where platform as a service means deploying "consumer-created or acquired applications" onto the provider's cloud infrastructure using the provider's languages, libraries, and tools.[1] CPaaS rarely works that way, since your application usually runs wherever you already host it and calls the provider over HTTPS. The term is a market category rather than a formal service model, which is part of why capabilities under the CPaaS heading vary so widely between vendors.