It's different from state to state, and even school to school.
My daughter started gifted in first grade. At that time, it was "enrichment" - project and research based, no extra homework, 90 minutes per day.
Starting in second, it was academic. They did everything in their gifted class except science and social studies.
In third grade, they did everything, including science and social studies and "specials" in gifted.
This year, in fourth, they do all academics in gifted and go with their home room for specials.
Some schools may only offer extra work in their regular class, and others may only pull kids out for enrichment once a week. Apparently our school system offers some kind of enrichment as opposed to academic gifted but I don't know anyone who has ever taken that option.
They typically work at least a grade level (but often many more) ahead, the classes move really fast, and there's more homework and so many more projects.
What I have NOT found is any help with organization. In my own experience, gifted children aren't necessarily, or even often, more mature or organized than kids in typical classrooms. I wish they could get some help with organization (some teachers may include that, but so far my kid's teachers have not. It's very sink or swim, figure it out yourself).
If you feel like your child is being pushed into the wrong track, and so does he, definitely talk to someone! If organization is the big problem, that's something he can work on!