They are completely different things.
The events-driven paradigm means that an object called an "event" is sent to the program whenever something happens, without that "something" having to be polled in regular intervals to discover whether it has happened. That "event" may be trapped by the program to perform some actions (i.e. a "handler") -- either synchronous or asynchronous.
Therefore, handling of events can either be synchronous or asynchronous. JavaScript, for example, uses a synchronous eventing system.
Asynchronous means that actions can happen independent of the current "main" execution stream. Mind you, it does NOT mean "parallel", or "different thread". An "asynchronous" action may actually run on the main thread, blocking the "main" execution stream in the meantime. So don't confuse "asynchronous" with "multi-threading".
You may say that, technically speaking, an asynchronous operation automatically assumes eventing -- at least "completed", "faulted" or "aborted/cancelled" events (one or more of these) are sent to the instigator of the operation (or the underlying O/S itself) to signal that the operation has ceased. Thus, async is always event-driven, but not the other way round.