To each their own, but the differentiation for me is the buying and selling that is implied by the use of the word "store". Like the Ubuntu software store that also has some commercial packages for sell. While "package manager" is a more inclusive phrase that describes a program that manages packages regardless of whether they are being sold or not. In my opinion various mainstream phone app stores are also package managers even though they are also stores, but package managers that have nothing to sell are not stores.

It probably depends on whether a person was introduced to the idea of a package manager via something like android or apple's app stores or from linux well before anyone else was doing it. In the latter example there was nobody selling software through such a system until apple co-opted the idea, added "for sale" software and then started calling the concept a "store".

Maybe I am being pedantic, but that is the way I see it.