The biggest difference between relays and contactors is current-carrying capacity.
Feeding power to motors and other equipment is a job for a contactor, relays rarely have ratings more than 20-30 Amps and don't handle inrush currents very well.
Control is another issue. The contactor can be closed by a pushbutton, but then you have to stand there and hold it depressed to keep the contactor closed. The contactor can be closed by a switch, but then how do you stop it remotely? Virtually all control systems use a contact from a small relay to close the contactor.
A pushbutton can easily be wired to close when a pushbutton is depressed, and STAY closed when that button is released. Opening the contactor only requires that the relay be opened by some method, which will usually include current sensors, limit switches on covers, emergcny switches, and a whole raft of other devices.
Also, since the only thing that the contactor does is close when power is applied to (2) wires, it can be in a separate compartment from the rest of the control circuitry; making everything safer for troubleshooting any problems that may arise.
