Terminology for third-party modules is confusing

This issue has been migrated from [#12186](https://github.com/matrix-org/synapse/issues/12186).

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Currently we have a module _system_ (or _interface_) where modules can register _callbacks_ and use module _API methods_, which are different things. It feels like we keep confusing them, for example calling a module callback a module API (which is even more confusing because it technically _is_ an API but just isn't a method of the `ModuleApi` class).

We need to figure out a better terminology.

The issue mentions the module system/interface, module callbacks, module API methods, and the ModuleApi class, but no files or tests. Start by locating those entry points and cataloguing how each term is used. Done means agreeing on clearer terminology and applying it consistently across the relevant module documentation and code references.

Written by the indexing model from the issue text.