A housing chain is formed by a number of buyers who are each dependant on selling - another party buying their existing property - to move forward with their own purchase.
A has to sell before they can complete on B's house.
B has to complete their sale to A before they can buy C's house.......& so on. If one sale falls through the whole chain will collapse.
I think both phrases mean the same thing. The seller is not waiting on the sale completion to buy another house. For example if a parent dies or goes into care their house would have no chain when sold. First time buyers are not part of a chain either.