In IBM BPM, Event-based Activities & Subprocesses are a little different than Ad-hoc Activities & Subprocesses, in how they are started.
Event-based Activities / Subprocesses are triggered by specific events -- like message arrivals, timer expiration, exception or error events, and so on. The triggers are defined and configured at design-time.
Ad-hoc Activities / Subprocesses are launched by explicit end-user action. A user starts the Ad-hoc activity / subprocess from a menu in the Process Portal (or equivalent).