Thank you. That is how it's set. I may not be doing a good job explaining it, or maybe I haven't figured out how to get the X to respond correctly.
With the 7, if I click the side button it doesn't unlock but it shows all the notifications.
With the X, I get only message notifications unless I unlock And that's actually another frustration (not a big one, but it's there): you're obviously looking at the phone when you do this, and quite frequently the X unlocks, and if that happens I need to get notifications with the downswipe from the upper LH corner, which is generally a two-handed task. Because, yet another friction point, reachability does not work consistently (didn't on the TouchID phones, either, for me - YMMV).
None of this is deal-breaker stuff, just UI/UX annoyances.

And the 7 and previous weren't perfect, either. Going back and forth between the two, trying to figure out if I'm going to keep the X or wait until the iPhone XI, I realize that there are some parts of each that I really like, and some parts that are meh or worse. Fortunately it's not going to ruin life, it's just a phone!