An OpenAI-compatible API is a service that accepts requests in a format similar to one used by OpenAI's API. This can let an app connect to more than one provider without changing every part of its code.
Think of two plugs that share the same shape: one may fit several devices, but the devices may not do exactly the same things.
“Compatible” does not mean identical. A provider may support only some options or may behave differently, so check its own documentation before relying on a feature.