Both are JVMs and are available not only for the latest stable JDK major version but also for earlier major versions like JDK 8 and others as supported products.
Zing's typical use cases are applications with requirements regarding low latency response time or huge heap sizes in the range of hundreds of GBytes or both combined. Zing is limited to Linux x86 64 bit. Zing includes its own Garbage Collection implementation (C4) and its own JIT compiler implementation (Falcon).
Zulu covers 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.