I read the OP's question to be asking if all the pumps are the same, not are they supplied with the caravan.
Let me answer the first point. There are several different manufacturers of caravan water pumps, and there is no standard design for the fittings, so you have to get the correct pump and plug to fit the system fitted in your caravan.
If you are buying a brand new caravan, the the correct pump and lug should be supplied with the caravan.
But there is not telling if the pump will be supplied with a second hand caravan. You would be wise to contact the seller to find out if a compatible pump is being supplied with the caravan, and if not then ask the seller to get one.
If th e pump is one that drops into an external water container, it might be worth obtaining a spare one to take with just in case. Having a pump fail in mid holiday is an annoying inconvenience.
Do read up about how to use the water system, becasue with a submersible pump, its important not to let th e pump run dry, as it relies on the water flow through the pump to cool the motor, if the the water runs out, the motor can over heat and damage the pump.
Many caravans use a pressure switch to monitor the water pressure and to turn the pump on and off automatically. Do read up on how to adjust the pressure switch.