I'm referring to questions like this one: Mapping reduction to show NeverHalt is undecidable
I understand with Turing reductions, you have to use oracle calls of the unknown language you're trying to prove is undecidable to solve a known undecidable language.
However, with mapping reductions, am I right in assuming these calls aren't needed? In addition, in the link provided, the solution pseudocode says
For input x: Simulate M for input w if it accepts, loop if it rejects accept x
How can you say "if it accepts"? How can you determine this, what if it loops forever and this is never found out? Why can you make such statements with a mapping reduction but not with Turing reductions? Could I make a statement like "if M halts on w, do ...". I mentioned this to my teaching assistant and he said you can't make any statements like these unless you're accessing an oracle and doing a during reduction, but I see loads of examples which seem to show otherwise. Hopefully this makes sense