Should drywall used on a ceiling be of a different weight/grade than drywall used on walls?
Depends on the ceiling/wall function. In most cases for repairs you want to replicate what was there, unless you are ripping the entire wall/ceiling or it's too hard to track down matching replacement drywall.

If the wall/ceiling is a firewall, you normally need to replace the structure that was there, which may be double-layer 5/8 type X ("firecode") gypsum. I prefer it for ceiling applications anyway (single layer where double-layer is not needed), as it's far less prone to sag than the thinner grades. It's also heavier, which you may not be fond of - and it is sometimes used on "acoustic" walls for that reason.

I've dealt with old walls that use as little as 1/4" drywall. 1/2" is what's normal/standard in new construction - 1/4 and 3/8 may be available from a supplier but I would only use those for repairs of a wall starting with that thickness where replacing the whole wall doesn't make more sense.