How do comic book stories work

"Does each comic have a different story to it?"

Yes and no. Some are singular stories that begin and end in one issue. other times a few issues will be part of an arc that either goes through one comic; example: Detective Comics vol.1 #s1-6; or cross over into other comics, either intercompany or within a characters spin-off or related books; like say it's a story titled Batman: blah, blah, blah. Issues included could be Detective comics #148, #150-151, Batman # 173-174, Nightwing #27, Catwoman # 8, you get the point. So all those issues would make up the arc. Sometimes maybe it crosses into another character's book so perhaps Green Arrow shows up so for in Green Arrow #118, that issue makes up part of the arc. For an intercompany arc, there maybe some one shots that act as a prelude, then the main story #1-6 (for example) and maybe a spinoff that goes into a character or characters' book(s), some one shots or miniseries that is a companion to the main story and then sometimes aftermath stories and one shots.

Numbering was originally for referencing and collecting although they try to sway readers with the "#1" or using buzzwords like relaunch.

For a character like Spider-man, Iron Man, Thor, you don't have to read every issue, but you should try to read the big arcs that get referenced even today. For instance, Gwen Stacy's death or Spider-Man No More in the case of Spider-Man or Demon in a Bottle or Armor Wars for Iron Man. thise are just a few for those characters, there are many more. For DC, they rebooted their history in 1986, so in the case of Batman, his post-crisis origin by Frank Miller was depicted in Batman #s 404-407 as Batman: Year One. So going back all the way to Detective Comis vol. 1 #1 or Batman vol.1 #1 you would be reading the Earth-one Batman which is a different Batman from the main continuity. From 1986 on, the stories in both Detective Comics and Batman are for the most part, canon, along with the stories from Shadow of the Bat, Legends of the Dark Knight, Streets of Gotham, Confidential, Batman and Robin etc, etc, are for the most part all canon. You can read them all, or you can read the big, infamous arcs all of which give you a firm grasp of his and his supporting casts histories since the 1986 reboot.