Do the jobs that give partial pensions after 3 years start paying that pension immediately or only after the person turns 65?

In the case of the council members, do their pension payments start after 8 years or after they turn 65? That makes a difference for sustainability in the long term.

For example, the police are vested after 10 years. If they leave after 10 years, they will get a small pension after turning 65 years old. They are fully vested after 25 years. That means that after 25 years of service they get pension payments regardless of their age. Someone correct me if I’m wrong please.