All are JVMs and are available not only for the latest stable JDK major version but also for earlier major versions like JDK 8.
Azul Platform Prime's typical use cases are applications with requirements regarding low latency response time or huge heap sizes in the range of hundreds of GBytes up to a maximum of 20 TBytes or both combined. It is limited to Linux x86 64 bit. Azul Platform Prime includes its own pauseless Garbage Collection implementation (C4) and its own JIT compiler implementation (Falcon).
Zulu and Azul Platform Core cover more general use cases as it is mainly OpenJDK with its Garbage Collectors like CMS GC, G1 GC, Parallel GC and the Hotspot JIT. It is available for a large variety of CPU architectures and Operating Systems from servers over desktops to embedded systems.