You’re broadly right- basically it’s September through about May- it coincides pretty closely with the generic school year, although I don’t know if that has anything to do with the scheduling.
Basically there are a fair number of weeks where new episodes aren’t shown- pretty much any week with a holiday, special event of some kind, etc… So in practice, even though there are 22 episodes, they actually take more than six months to actually broadcast them.
This sort of thing used to be nearly ironclad- new shows started within a fairly narrow window in the fall, and ran straight through with the few exceptions until late spring. In recent years, with cable competition, they’ve started varying it a lot; some shows will do maybe 10-11 episodes, then have a mid-year hiatus in the winter, and pick back up in say… April and run through June or July. Others will do a smaller-scale version of that and take breaks of 3-6 weeks between new episodes, and end up finishing later than the traditional time.
In addition, US television has very fixed times- shows typically have a single weekly time slot- this may vary between seasons, but very rarely varies within a season (and is usually a sign the show is not doing well). For example, “Friends” started at 8:30 pm Thursdays in its first season, which was right after “Seinfeld”, and moved to 7 pm Thursdays for the remainder of its broadcast run.
Which brings us to the next difference - US tv scheduling is a sort of game that is played between networks based on who, what and when TV shows are watched. They tried to basically engineer things such that people didn’t want to change the channel- having “Friends” at 7 and “Seinfeld”/“Frasier”/“Will and Grace” at 8, and “ER” at 9, with lesser comedies in the gaps meant that for a certain young adult demographic, NBC on Thursday nights was a destination at the time- people talked “around the water cooler” about those shows, so people made a point to watch them, and ended up watching stuff like “Just Shoot Me” or “Veronica’s Closet” through inertia.
Meanwhile, shows like “Firefly” or “Futurama” were in time slots that weren’t conducive to long-term success, and ended up cancelled on their original networks, only to be revived on other networks or in other formats.
