I was about to write up this exact post, almost verbatim. Excellent game sense can seem like you're able to predict the future. Someone who thinks they're "bad at FPS games" usually runs into a lack of game sense, but mistakenly blames it on bad reflexes.
I mean it can be both. Some people really struggle with that level of hand eye coordination. That's one of the reasons I really appreciated Overwatch. It gave a lot more options to play well that didn't require the ability to click on heads at all. This doesn't just help uncoordinated or less experiences players, but also players with disabilities of various sorts. The character Mercy for instance has a beam which heals or boosts damage but it locks onto a player so tight aim is rarely ever a concern and game sense becomes almost everything.
Which seems easy to confuse. If you don't have good game sense, you'll get into situations where you feel like you need twitch sense, so you'll want to think that's your failing.
