Position is the entire grammar here, and the two positions are not related in meaning. Before the verb, ได้ is about whether the event happened. After the verb, it is about whether you are able or allowed to do it.
This is the single most productive trap in the middle of the course, because both versions are extremely common and the words are identical.
- ไม่ได้ไปmâj.dâj paj
did not go
before the verb: a plain negative past
- ไปไม่ได้paj mâj dâːj
cannot go
after the verb: ability, blocked
- พูดได้pʰûːt dâːj
can speak
- ได้กินdâːj kin
got to eat
before: it happened, and often that you were lucky it did
The half that is free
The post-verbal ได้ covers both ability and permission, exactly as pouvoir does in French. You will not feel that ambiguity because you already live in it.
What is not free is the pre-verbal one. French puts the past on the verb itself, so there is no French habit to lean on and nothing to transfer. It has to be learned as a position.
And ได้ on its own
As a bare verb it means to get or to receive, which is where all of the above comes from: something you got to do, something you have the capacity to get done.
You do not need the etymology to use it. You do need to stop treating ได้ as one word with four meanings and start treating the position as the word.