A masters thesis is a few month's work from an untrained student going through an idea that's already being explored by the school's research group. A PhD typically involves far more deep independent work that's deemed relevant by at least one research institution.
In my experience, a master student's final project typically constitute their first foray into / encounter with academic research. So yes, untrained in that sense.
The fact that you are paid doesn't preclude it being a traineeship.
No not really. A PhD student at most receives a scholarship, and currently at least in Europe has to undergo a curricular part comprised of a dozen or so courses. How does that not count as schooling?
If I'm not mistaken the only exception to the schooling requirement is if a student is able to publish a few research papers on a topic that are coherent and related to a concrete research topic that could support their thesis.
I don't know what could possibly lead you to believe that someone just starting off his master's thesis has any experience whatsoever in research, and has any contact with any academic topic beyond the standard curriculum that every single one has to go through to get a degree.
Does that count as experienced in your book?