In shmups, bullet logic/movement can either be contained to the world space, or the screen space.
Bullets that exist in the screen space will always exist relative to the screen's location no matter what's going on with the game's scrolling. So let's say an enemy shoots an unmoving bullet that just stays there - it will always stay at the exact same spot of the screen, for the entire stage, no matter what the stages or players do.
World space bullets are a bit different, they move around together with the game's scrolling logic. So if that same enemy shot a stationary bullet, it would move down, or maybe left, or even backwards, depending on how the game's stage scrolls.
Both styles of bullets have their pros & cons. Because world space bullets scroll, it means that their aiming gets completely fucked - they're only able to shoot at the spot the player was a bunch of frames ago, and as a result they can never hit the player unless they lead their shots, or the bullet speed/player hitbox ratios are unforgiving enough. Screen space bullets have an issue called bullet wobble - the disconnect between bullets and world scrolling can be really unintuitive, especially when playing co-op.
Because of the fucked up aiming, world space bullets are a lot more risky and should be handled with care. Importantly, beginners often default to world space because scrolling the player/camera through the level feels more intuitive to them, rather than because it's a conscious choice they make after weighing the pros & cons.
CAVE use both styles of bullets in their games - bullets fired by most ground targets will exist in the world space, bullets fired by air target will exist in the screen space. Not only does this create a subtle enemy distinction, but it also helps create more consistent looking patterns for ground enemies. If you've ever wondered how CAVE do those straight lines that tanks shoot - this is it. It's not actually any sorta predictive math or anything, they are just world-space objects. Because the enemies can only shoot in a preset number of directions, the fact that they can't aim precisely at the player doesn't matter all that much, if anything sometimes it helps them compensate for the inherent imprecision of the directional lock.
