The meaning of Afterschool or after-school is more or less the literal meaning of its components; per AHD:
1. Taking place immediately following school classes: afterschool activities.
2. Of or being a program designed to provide care for and educational enhancement to children in the hours immediately following school classes.
An afterschool program.
Thursagen may have accidentally omitted a word, intending during after-school hours or during after-school programs, but only Thursagen would be able to say for certain.
If the phrasing was intended, then during after school and after school can indeed mean different things. In the first, after school refers to some set event or activity that takes place after the end of classroom instruction, which has a set start and finish time. The latter refers to any time after the end of classroom instruction.
For example, my high school's formal instruction ended at 2:05 p.m., and activities like sports practice, drama rehearsal, and so on began at 3:00 p.m. to allow for 45 minutes of study hall and 10 minutes of walking. If I told some students that I planned to walk home during after school, they would likely assume I meant I would walk home some time between 2:05 and 3:00p.m. If I told them I planned to walk home after school, then I might be walking at any time after 2:05 p.m.
I will add that afterschool as a noun sounds terrible to my ears, and I myself would only use it in rapid, informal speech as a shorthand.