If the process you're trying to describe is complex or can be looked at in two different ways, you can explain it pretty much in those words. Because inside your story, the same tension and double-definition exists - so that can be how people think of it and describe it.
Consider these two possibilities:
If the nature of the convergence is widely known and understood, than the double-definition is the definition. If everybody thinks of it both as a merger and an on-going process, then that's how you introduce it to begin with. You give it a particle-and-wave type of explanation, introducing it right off the bat as something counter-intuitive yet well-understood. For example:
Even though the convergence seems to have happened already, the fact is that we're all still converging. In one sense, it's an event that happened in the past - in another sense, convergence is still taking place, all around us, all the time. As our technology advances, our ability to keep the convergence up and bring us together keeps advancing right along with it.
On the other hand, if the nature of the convergence is unclear, and only gradually uncovered to the reader, it's absolutely fine to start out using one explanation -- a partial explanation -- and only later come back, explain what we were missing, and reveal to the reader that the first explanation was a partial one. The risk you describe -- that you might confuse your readers -- is a real one, but you can avoid it: all you need to do is make clear that the new explanation is supposed to be surprising and disorienting. Then they know that their confusion is justified, that they're reacting correctly to the information in the story - instead of suspecting that the confusion is because the author isn't being clear, or because they haven't been following along closely enough, which are considerations from outside the story world.
One very clear way to do this is to make sure your viewpoint characters do not know about the later explanation. It's as much news to them as it is to the reader; that makes it very easy to understand that the reader is being called upon to revise his understanding of the setting - right along with the viewpoint character. This method might look like this:
"I don't understand," said Eddington. "What do you mean, we're still converging? We've already converged. We're here, converged. Isn't that the whole point?"
Well, said the AI it might seem like that, yes. However, the truth of the matter is, what you think of as 'convergence' was merely the very beginning of the process. [explain explain explain]
Another option is, you might want to divide the reader's understanding of the convergence into "simple explanation first/complicated explanation later" simply because the longer explanation might be difficult to work in well early on in the story, and isn't necessary until later. If that's what you're going for, you can let the reader tag along with a viewpoint character that knows more than he does. But you're going for pretty much the same effect - the viewpoint character offers the reader one explanation at the beginning, and intentionally provides a more complicated explanation later on. The main difference is that here the viewpoint character is (knowingly) surprising the reader, whereas in my previous example we had some other character (knowingly) surprise the viewpoint character (and the reader through him). This is a rather crude example:
Now, the convergence is a bit more tricky than just colliding our two realities together and calling it a day; I don't want to give you the wrong impression. A lot of it has already happened, but the truth is, it's still happening all the time.
In this case, what's very very important is that the reader not need that extra explanation until he gets it. In other words, you can get away with simplification as long as the simplification makes sense and isn't deliberately putting the reader at a disadvantage. (You can have some hints and "edges of ideas" to hint that there's more to convergence than you've said, but nothing big or crucial.) It's basically the narrator going: OK, I've taught you how to send email; now I'm going to teach you how the internet works. It's all right to expand gradually outwards, just make sure the reader is never left at sea and bewildered just because he hasn't gotten the full explanation yet.
Hope this is clear and helpful :)