I think your intuition is mostly correct when it comes to modulation. I would make only one small adjustment: most scholarship tends to view a change in tonic as different from a change in mode. In other words, moving from C to G is a modulation because we change the tonic pitch, but moving from C major to C minor is "just" a change in mode. Thus we see that "using new pitches" isn't enough to effect a modulation, it's actually changing tonic. (By this logic, one could say that changing from C Ionian to E Phrygian is a modulation, even though there are no new pitches.) As you've suggested, modulations—especially in music of the common-practice period—tend to return to their home key.
A key change can be one of two things. It can either be a physical spot in the score—the key signature changes here from C major to E minor—or a moment when the music leaves one key and moves to another one (either with or without an explicit key signature change). I think it's often a bit like the square vs. rectangle issue: not all explicit key changes in the score are modulations, but I'd say that all modulations are key changes.
You'll notice that "key change" in this latter sense (moving to another key) is thus synonymous with "modulation." I don't personally see any clear distinction between the two in terms of relationship to the prior key and whether or not that prior key will return.
Tonicization is often taught as a brief foray into another key. There's usually some gray area here in terms of how long a tonicization must be before it becomes a modulation, and it's only made worse when we discuss notions of "extended tonicizations." But I think there's a very good rule here: if there's no cadence in the subsidiary key, it is not a modulation, but a tonicization. Once we use this cadential rule as a limiter, it becomes much more clear when something merely tonicizes and when it actually modulates.
Lastly, all of these are further confused when you read past theory treatises. Many authors of yore use "modulation" the way we currently use "tonicization," which certainly doesn't help at all.
(Thought-provoking question, as always!)