Is a CRUD application always an API in the web world?

Since in about 99.9% of tutorials, posts and forums, whenever the word CRUD gets in stage, the word "API" immediately follows it, I wasn't able to find the answer to my doubt: Is every web application with full CRUD functionality an API? or can I actually code a CRUD web application that's not considered an API?

All these doubts make me wonder of the early days of web development, where people would use the front end to send requests to a server, then the server would create/query/modify/delete DBs/files based on a specific (let's say) button being clicked...were those still called "CRUD APIs"?

Or is a CRUD only an API when there's no direct calling of the model's methods? (it needs, let's say, a controller code that'll ensure that the correct input and request have been made before sending the instructions to the model that'll actually do the CRUD work)