These are somewhat imprecise terms. They are used when a customer wants a pair of contacts which open or close for a signal/control state, but are completely insulated (up to say mains voltage) from any other circuit or supply potential or earth/ground.
This ensures there is no unwanted interaction between equipments.
"Potential Free" is ambiguous - some might think earthing a contact made it potential free!!
"Dry Contact" may refer to a circuit in which current or voltage are so low as to require special contacts like sealed reeds or gold/platinum contacts to get reliable low ON resistance.