In the original Fate visual novel/eroge, there are 3 different routes that are possible, each based on a female character. Each route is given a suffix to identify it, and the anime adaptations added this suffix to specify which route they are adapting. Studio DEEN adapted the Saber route which has the “Stay Night” suffix, and thus named it Fate/Stay Night. Both Studio DEEN and ufotable adapted Rin’s route, and thus Fate: Unlimited Blade Works. Lastly, ufotable also adapted Fate: Heaven’s Feel, which is Sakura’s route.
Correction
Um actually … The visual novel is called Fate/stay night thus the last 2 anime adaptations are called Fate/stay night: Unlimited Blade Works and Fate/stay night: Heaven’s Feel accordingly.
Saber’s route is suffixed with “Fate”. Thus if we were to follow the suffixing logic for the first anime series, we would get Fate/stay night: Fate. This confusing title may be why the first anime adaption dropped the route name.