EDIT: This answer does not answer the question as asked, due to fact that I misinterpreted the question as it had been phrased at the time. However, I leave my answer up for perusal for those who might find it useful
For clarity, I will rephrase the meanings and number them like so:
(1) Stop action A to do action B
(2) Stop action A to do action B, then return to action A after action B is finished (In other words: pause action A to do action B)
I believe the reason why you found meaning (1) more often is because the pausing of action B in (2) is implied or not stated explicitly. You can guess if you mean (1) or (2) by the duration of action B, but sometimes you could mean both, and that's okay. If the person you're speaking to really wanted to know whether you mean (1) or (2), they could ask you in the course of the conversation.
Take the following sentence, for example:
I stopped playing games to do my homework.
If someone said this to me, it is ambiguous enough that they could mean (1) as in they stopped playing games to do their homework, and we don't really know if they continued after or (2) they stopped playing games, finished their homework because they had to and then went back to playing games. If I really wanted to know which one they meant, I would ask them "Did you go back to playing games after you finished your homework?" and they would say "yes" or "no", depending on what they did.
However, if action B is something that is of a short duration, like drinking a glass of water, then it quite likely that you mean (2). This shows you that context really helps with figuring the intended meaning.
I stopped exercising to get a drink of water
The context shows that I mean (2). Exercising made me thirsty, so I got a drink of water so that I could continue exercising. Perhaps this also shows that action A creates a need for action B, where action B is the person's solution or remedy for a problem caused by action A. And yes, even with the example mentioned in the comments - for some people, the solution to stress (action A) is to go smoke a cigarette (action B).