When electromechanical relays were still used, inverse time relays, definite time relays, and instantaneous relays were separate relays.
Modern protection relays combine inverse time, definite time, and instantaneous characteristics into one device. So you can have all three types in one device.
The difference between inverse time, definite time, and instantaneous relays
The time-current characteristic curve is different for inverse time, definite time, and instantaneous relays.
You can use combinations of curve types to achieve the design requirements. I commonly use inverse-time, definite-time, and instantaneous elements, all on the same relay.
Inverse time overcurrent relays: Slow to trip at low currents. Faster to trip at high fault currents. Used to co-ordinate over load protection, which may have a high starting current. Generally the most sensitive (lowest amps pickup), and slowest to operate.
Definite time relays: used to co-ordinate over other definite time, or instantaneous protection. Generally less sensitive (higher pickup) to prevent operating for load inrush. Generally faster operating time.
Instantaneous relays: Used when co-ordination is not required. Usually the least sensitive of all relays, as the relay must not operate for any kind of inrush, or operate before any downstream relay.
For more details, including application details, refer to:
Power systems protection is a deep and interesting field. Good luck!