Creatures and Units may always fire their ranged weapons the same turn they moved as long as their APS allow them to do so.
When a creature is riding an Animal đž or Ground Vehicle đ, this is also the case. However, if their mount or ground vehicle moves, they will gain a Hard DM to all ranged hit rolls, unless a special effect states otherwise or the vehicle's weapons are Stabilised. This is meant to simulate the significant impact that firing on the move has on any ground vehicle, even at low speeds, at least with any degree of accuracy.
Weapons fired from an Aerial Vehicle đŠī¸ or Naval Vehicle đĸ on the move do not suffer from any penalties.
A careful observer might note that, in a standard 3 APS turn economy, the Move (1 APS) Regular Action can be paired with either Reaction Fire (1 APS), Overwatch (1 APS), Aimed Fire (2 APS), Suppressive Fire (2 APS) or Indirect Fire (2 APS), but if the Creature also performs a Sprint (1 APS), their only options are Reaction Fire (1 APS) or Overwatch (1 APS). This design choice is set up in such a way that sprinting while firing accurately becomes impossible, unless the Creature possesses 4 or more APS, which would make them, by all accounts, superhuman.