Your thinking seems to be correct for the majority of cases but as it usually happens in life there are exceptions to the rule. For example, there can be combinations of those, one request would be doing two things at a time. It is not uncommon to have POST doing some modifications on the server and at the same time retrieving information to be displayed or fetched. In some cases this is not good practice but sometimes I allow this - for example, a POST request to save a form which ended up with invalid input data - the POST request may re-display the form for the user to correct.
And there can also be actions that do not fall into any of the 4 request methods. For example, “SEND” - submitting a form sends the message somewhere - it doesn’t update or create anything, it sends. Of course, there can be a mixture of sending and storing in the db but the the very action of sending doesn’t fall into any of these categories for me.
There could be many more request methods outside these 4 if you think outside the realm of a web application: SHUTDOWN, RESTART, SLEEP, SHUT_THE_DOOR, TURN_ON_THE_LIGHTS, PLAY_MUSIC, FLUSH_THE_TOILET, DETONATE_THE_BOMB or whatever you imagine a computer accepting http requests were able to do.
I would say for general web applications such exceptions are rare. But we need to keep in mind that sometimes a http request might have to do something different that any one of these 4. I’ve read that it’s possible to invent any request method and use it with XMLHTTP but I’ve never tested it.