A trap is an exception in a user process. It's caused by division by zero or invalid memory access. It's also the usual way to invoke a kernel routine (a system call) because those run with a higher priority than user code. Handling is synchronous (so the user code is suspended and continues afterwards). In a sense they are "active" - most of the time, the code expects the trap to happen and relies on this fact.
An interrupt is something generated by the hardware (devices like the hard disk, graphics card, I/O ports, etc). These are asynchronous (i.e. they don't happen at predictable places in the user code) or "passive" since the interrupt handler has to wait for them to happen eventually.
You can also see a trap as a kind of CPU-internal interrupt since the handler for trap handler looks like an interrupt handler (registers and stack pointers are saved, there is a context switch, execution can resume in some cases where it left off).
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