Here's a quick distinction that I probably won't be using much myself but is worth making nonetheless. It's internal vs external depth.
Internal depth is the depth a game has as a formal system. It's how complex ingame interactions are when you are following the built in, formal rules and goals. You can check out Celia Wagar's writing on depth if you want to get a clearer, extensive picture of what depth is.
Games might be beautiful little logical systems, but unfortunately humans have to engage with those systems too. In fact some might even argue that's the point.
That's where External Depth comes into play. External depth is the stuff happening outside of the game that nonetheless feeds back into your in-game actions.
They are the mental processes that you go through - various heuristics n models you use to break down and figure out the problems games present you with (puzzle games, reading shmup bullet patterns). And they are the actual, physical interactions you have with games (how you move your mouse, how you move your fingers, your controller grip, what you look at and when).
Think of puzzles - they have next to no internal depth, but the way your mind works through different paths to arrive at the solutions has enough variability to make them really interesting to solve. Then think of rhythm games - again, no internal depth, but a lot of variability in how you move your fingers, how you read the notes, even how you remember the maps and move your eyeballs, etc. Fighting game/CAG combos & something like NES Tetris also have really clear real-world "tactical" element as players discover better ways to optimize inputs, from plinking inputs to sliding across buttons to the rolling technique used in Tetris that I'm sure everyone's familar with by now.
Playing instruments and slowly learning better habits and techniques makes external depth very noticable.
All games are a mix of internal and external depth, and just cuz a game seemingly has no internal depth doesn't mean it doesn't have a very rich deep meta game elsewhere. If it's engaging, then there's something there, even if it isn't obvious.