Creatures may always fire their ranged weapons the same turn they moved as long as their Action Points allow them to do so.
When a creature is riding an Animal 🐾 or Ground Vehicle 🚗, this is also the case. However, if their mount or ground vehicle moves, they will gain a Hard DM to all of their hit rolls, unless a special effect states otherwise or the vehicle's weapons are Stabilised.
Weapons fired from an Aerial Vehicle 🛩️ or Naval Vehicle 🚢 on the move do not suffer from any penalties.