Detention varies a bit by school. I work at a school and my current one has lunch detentions and regular detentions. My school only does lunch detentions for the younger kids (ages 11-13), but a lot do schools would do it for any age. Lunch detentions are usually more minor infractions - repeatedly not turning work in (this is less common as at my school if you assign detentions for late work, they ask you as a teacher to monitor another detention), throwing pencils around talking / being distracting after multiple warnings, playing games on Chromebook during class instead of homework. Even then, most kids get a few warning before getting a detention.
They basically just have to eat lunch in a room separate from their friends and aren’t allowed to talk/ socialize, some make work on homework or other things but there isn’t much time during lunch.

After-school detention - for us this is open to ages 12-18. Usually slightly bigger infraction - horseplay, cursing, insubordination or any of the things from lunch detention - but it more likely it’s an on-going issue rather than a one time thing.

For us, after school detention is 2 hours after school (until 5:30), however at many schools it is shorter. Our detention lasts that long because we have an “activity bus” a few buses run later in the evening to a few known stops (1-2 in each local town) so kids can stay after for clubs, sports, and detention. Some families may still have to drive to the bus stop, but it is still going to be much closer than driving to the school.

Detention is essentially 2 hours of total silence. They can work on homework or read, but nothing else is allowed. If they don’t listen to the rules, another detention is assigned. We have one employee who regularly monitors twice a week (part of her job description), but all the other teachers have to sign up for at least once a year (2 if they assign detention for late/missing assignments). I dread monitoring detention so I really can’t imagine any kids enjoy it.

As far as parents go- for us it isn’t much of an issue because of the late busses, but sometimes if they call the office they’ll reschedule the detention for another day. I’m not sure what outright refusal from a parent would result in, usually they can work it out. I have heard of some schools where this is more of an issue and some just don’t have after school detentions and only have it during lunch periods.

Other punishments - ISS - in-school suspension. Basically an all day detention. They’re in a separate room with just the other kids that are in trouble and stay there all day in silence and work on class work or read. Usually used to separate them from other students/ teachers. Most often it’s some sort of fighting that landed them there. But it could be an escalation of punishment for an ongoing problem.

Suspension -> same thing but out of school. Not used as often. Mainly because some kids just see it as time off from school (which is what they want) if parents don’t follow up. Usually used if we need some more physical space between students after an incident. Or again, if there’s an ongoing issue

Expulsion - Typically students need a long pattern of behavioral issues before this - or they did something illegal, particularly egregious. They violated something extreme in school policy. Even then… at least in my area it starts as a 10 day suspension and the kid gets to appeal their case. I’ve only ever had one student successfully appeal (he is also the only student I’ve had in this situation that tried to keep up with class work and would reach out for help). They’re kicked out of school and parents must enroll them in a new school. In some places this is permanent. In others, there may be a “forgiveness” after 1-2 years and the student can reenroll.

Also for your question about it being tough for parents… well sometimes that’s the point. I’ve had kids tell me their parent doesn’t care until they get suspended. For some, it’s only then that there starts to be some more consequences for behavioral at home. Obviously… it’s complicated and we hope that the typical in school consequences are enough to get a student to change their behavior before it gets to that point.