You don't say where you live or which potentillas you have, but if they are both the same variety and the one without flowers has leaves, it could be that the one without flowers will bloom later in the season. If the one with no flowers also has no leaves, then it might be dead. It sounds like you purchased them late last summer, so you still have time to see if it blooms.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.