Both are applied under pressure.

Shotcrete is a wet mix. A concrete truck delivers a load of concrete pre-mixed and it is put into a pump that allows the material to be "shot" in a wet state.

Gunite is delivered in a hopper truck as a dry material with 2 compartments holding sand and cement. The auger mixes the material in the proper ratio and sends it to a pump in a dry state where a nozzle at the end adds the appropriate water.

Either method is acceptable. Gunite may give a bit more freedom on a hot day as concrete in a truck can set up just sitting. It comes down to a contractors preference.

Not sure about price differences in your area.