I don’t think that “bullet hell” differs from shmups so much as it is a subcategory of shmups. A “bullet hell” shmup is a specific type of shmup where there are an overwhelming number of shots on the screen to dodge.

I’m sure that it’d be perfectly-acceptable and appreciated to post here!

EDIT: Here, Wikipedia has a better description than I do:

https://en.wikipedia.org/wiki/Shoot_'em_up#Bullet_hell

Bullet hell (弾幕, danmaku, literally “barrage” or “bullet curtain”) is a subgenre of shooters in which the screen becomes crowded with complex “curtain fire” enemy patterns. It is also characterized by collision boxes that are smaller than the sprites themselves, to accommodate maneuvering through these crowded firing patterns.[29][30] This style of game, also known as “manic shooters”[7] or “maniac shooters”,[31] originated in the mid-1990s as an offshoot of scrolling shooters.[31] The DonPachi and Touhou Project series are early titles establishing the principle of bullet hells.[32]

Mark of the Electric Underground has a recent video about this that I thought was interesting. I tend to think that categories have really porous boundaries, in that every time someone tries to draw a clear, solid line, there’s almost always an exception.

Games like Vampire Survivors have been categorized as “bullet hell” which… I mean, maybe. But it’s not a shmup for reasons it’s hard for me to articulate. I actually tend to think of games with free movement and vast enemy hordes as musou games!

modern usage of the phrase “bullet hell” has been coopted by games that are definitely not in the shmup genre. we had this issue with the term “shooter” or “shooting game” back when FPS games became popular. It’s why we have the term shmup now, for better or worse.

I echo the sentiment that a bullet hell is a subgenre of shmups and, for me, it focuses on dense amounts of projectiles and micro dodging. when I hear the phrase I immediately think of titles like some of the later touhou games or the later bosses in dodonpachi games.