You're right. A star-delta (Y-delta) starter has two contactors, interlocked via their auxiliary contacts so that only one can be closed at any time, with a timer to switch from star to delta a fixed time after the motor has been started. You could make one from individual components.
Maybe you should check that you are comparing like with like. Does the starter you've been quoted a price on have extra protective relays (underload as well as overload, electronic protection, motor seal leak or oil in water detection, etc)? Will it be constructed to the same standards as the DOL starter you're comparing with (panel construction and compartment segregation, Ex-rated, some kind of additional mechanical interlocking mechanism between the two contactors)? Does it have extra controls (lamps, pushbuttons, remote comms)?
Maybe the price hike is partly because of the extra cabling requirements to the motor (6 cores instead of 3)?
Can't think of any other possibilities at the moment.... have you gone to more than one manufacturer for a quotation?