The TLFi has a full paragraph (Rem. gen. 3) explaining the generic difference between adjectives and substantives in -ant vs the ones in -eur.

The main idea is that -eur generally implies a function (intrinsic role) while -ant is more a property (activity).

One example would be the opposition between c’est un gagneur (he is a winner) and c’est un gagnant (he is one of the winners).

So the étudiants and dirigeants happen to study or manage more likely because they decided or were told or elected to do so while a chanteur an accusateur or a procureur have completed studies or trainings in order to sing or prosecute as their main occupation.

As dimitris suggested, a doctorant is studying (transient activity) while a docteur is a permanent title and chercheurs have decided to make research their main long term activity.

Note that the distinction is not always manifest, e.g.:

• Attaquant (striker) vs défenseur (defender)

• Voyant(e) (psychic) vs voyeur