A trap is a software or hardware exception in a user space program, which then context switches into kernel space and invokes the kernel exception vector, which then handles it.

A fault is a particular type of exception that usually occurs when the kernel is performing an operation on behalf of a user space process, and that operation is incapable of being completed. Depending on the context, the kernel may handle it by passing it to the kernel exception vector, or it may trigger handling directly.