Which scenarios would be better for one versus the other?
The issue with API is that it’s a word that is used whenever two services communicate to each other programmatically, and this happens often…
In this case, this two things are two completely different things:
the API connector is a tool that lets you add yourself some calls to use external services, either as action or data sources. So in other words, you Bubble app will interact with other services, and things will be triggered on the Bubble app’s end.
the Bubble API is a way to trigger a workflow in your Bubble app (POST) from the outside world. Or read some Bubble app data from the outside world (GET). In any case, this will be triggered by an outside app/tool, and that will either trigger something with Bubble or read Bubble’s database. So exactly the opposite as 1)
Generally speaking, using 2 is more technical than using 1).