Hi John,
I'm glad you brought this up. I have a post (here - off site) devoted to the word parousia. But the focus of the post is on whether the NT ever associates Jesus' parousia with his enthronement (as the WT does).
When I get a chance I am going to have to add a post discussing the differences between erchomai and parousia.
The first difference between these two words is that erchomai is a verb; parousia is a noun. Erchomai expresses movement, parousia is an event. And thus, the two words can be used in the same context, such as at Mt 24:36-44. The verbs in the context describing Jesus' "coming" (vss. 37, 42, 44) are all part of the event, his parousia. (vs. 39)
Parousia means "presence," but the way it is used in the NT and anciently gives it an added flavor that, to me, "presence" does not convey. It is more like an official state visit, with all that such a visit would include.
In the NT (as my link shows), parousia is associated with Jesus rewarding his faithful servants and punishing the others. Mt 24:27 associates it with sudden and widespread effects. And with death, such as one might find on a large battlefield. (Mt 24:28 - for which, see footnote # 38 in the NET Bible here.)
To me, "advent" much better encapsulates how the NT uses parousia. "Presence" doesn't carry any of those overtones. But I would say that "presence" much better encapsulates what the WT teaches about Jesus' parousia, that is, an invisible presence that only a few know about, something much different from how the NT presents it.