Are event and mode well defined terms in CS literature?
I'm not sure whether they have accepted meanings, but to the extent that they do, an "event" happens at an instantaneous point in time, as opposed to something ongoing.  If I was reading something that used the word "mode", I probably wouldn't be sure what is meant by "mode" without looking at the context.

I'm not sure whether you should expect precise, widely-accepted definitions for terms that are used informally.