Comment by Polizeiposaune

Depends on the processor architecture and its nomenclature.

Traps typically also result from exceptional conditions (like divide by zero or page fault).

An architecture may or may not provide non-trap paths for less-privileged code to invoke more-privileged subsystems (call gates, "syscall" instructions, etc.).

Traps typically need some way to preserve all userspace-accessible registers (otherwise resuming from a page fault is .. hard). Dedicated syscall instructions may only need to restore a subset of registers.

In some implementations, processors may discover that an instruction must trap after it starts irreversibly changing architecturally-visibile state; in cases like that, the processor needs to leave enough breadcrumbs for the OS to allow either a clean unwind or a resumption of the interrupted instruction. My understanding is that the original 68000 somewhat famously got this wrong.