The two sentences are different. The first is incomplete.
The first sentence means that David stopped doing something to talk to you. The second means that John no longer talks to you.
Your first sentence, and its given meaning
"David stopped [?] to talk to me." - David stopped so that he wanted to talk to me.
seem incomplete to me. There is something missing - it can be either of these:
(a) David was on his way to work. He stopped by [your house] to talk to you.
(b) David was perhaps eating, running, driving, or mowing the lawn. You waived at him. He stopped [the action] to talk to you.
Perhaps, the absence of "doing something" or "by" after "stopped" indicated to them that the sentence was saying that David stopped talking to you. They might have thought that "to talk" was an error in writing and that it should have been "talking"; that would make both sentences identical.
"David stopped talking to me." = "John stopped talking to me."
Note that this is very unusual:
"David stopped so that he wanted to talk to me."
It should either be
"David stopped [doing something - walking, cleaning, driving, etc.] so that he could talk to me"
"David stopped [...] because he wanted to talk to me."
- Do non-native speakers of English who are not advanced find the difference between the two sentences like the native speakers unless explained?
- Is [there] really a difference between the two or [do they] mean the same to non-native speakers who are not advanced learners?
both of which, in my opinion, cannot be answered without conducting a poll here. Even if a poll was carried out, the number of non-native participants in ELL would not make a proper representative sample of the non-native population.
Also, it would help if you defined "non-native speakers who are not advanced learners". Who is an advanced non-native learner - a non-native who went to an English medium school (with English curriculum) for 12 years? Or a non-native who immigrated to US and has been living there for 30 years?