Where to find vSphere Lifecycle APIs

I've seen a several questions both internally and externally about where to find the vSphere Lifecycle Manager APIs and the confusion stems from these APIs being found under ESXi rather than vCenter Server.

For vSphere Lifecycle Manager APIs and everything from managing cluster images, vendor add-ons, hardware compatibility and solutions, to remediating cluster images, you want the ESX Settings REST APIs. 

For vCenter Server lifecycle APIs and everything from interoperability and checking for vCenter Server updates, to pre-check reports, you want the vCenter LCM REST APIs.

Hopefully this post clarifies which API group is which.