Do different 68k simulators have different TRAP tasks?

The TRAP instruction just calls a routine that's pointed to by a longword somewhere in memory. That part of the behaviour is common to all 68000 CPUs. Where that longword points, and what the routine it points to does (and therefore how you pass it the data it needs and so on) depends on the particular system.

(The Atari ST for example used TRAP to call into the OS, and you generally passed all relevant information on the stack. The register contents were ignored. I believe Mac OS "System" used TRAP in a similar way, too, and the Amiga didn't use it at all.)

The 68000 provides 16 user traps (software interrupts/exceptions) but doesn't specify what they do. That is down to the system BIOS/OS, whether that be a simulator or Amiga, Atari ST etc. You can find a list of tasks performed by TRAP 15 in Easy68k at the bottom of this document http://www.easy68k.com/files/EASy68KQuickRef.pdf.