From what they've said, it sounds like they're genuinely trying to distinguish between a breakup and a hiatus - they're not calling it quits permanently, just stepping back indefinitely. That's actually a pretty common move for bands who need to recharge or deal with other stuff, but yeah, the wording does make it feel a bit ambiguous. The key difference they're making is that a hiatus leaves the door open to return, whereas a breakup would be final. Whether that distinction matters much in practice is another question though.
If you want to see them live before they go dark, you're probably right that there's a limited window. I'd check if they've announced any farewell dates or final shows before the hiatus kicks in. Bands usually do a last run of dates to say goodbye properly, so keep an eye on their social media and tour announcements. Worst case, you miss this window and they come back in a few years - but yeah, if they're important to you, catching them now would be smart.