where i'm from, a chase is something like a Tahoe, equipped with ALS gear and a medic. they will provide ALS back up to a BLS ambulance. if the call does not require ALS interventions, the ambulance takes the call and the chase car goes back in service. if the call requires ALS, the provider gets off the chase and goes in the ambulance and the EMT drives the chase car to the hospital.
its a way to keep personnel costs down. an ALS provider typically makes more money, having every ambulance staffed with a medic and with most calls being BLS, you would have an ambulance with a higher paid medic on it performing the same skills as an EMT.
it always comes down to money!