So I call one of the online stores looking for fins for my 50lb daughter and they lady helping me indicated that full foot fins were for snorkeling and open heel was for diving.
Is there any truth to this
This sort of categorisation is so simplistic. Back in the good old days, when money was more tight, any kind of fins were considered suitable for snorkelling and diving. It's often forgotten that the first fins used for snorkelling and diving in the post-war era were the kind now used predominantly by bodyboard surfers, all-rubber with non-adjustable open heels:
I expect the lady at the online store would be of the opinion that such fins would refuse to cooperate if used in snorkelling and diving, which is of course nonsense.
As for full-foot fins versus open-heel fins, it should be a matter of personal choice. When I first trained to dive in the mid-1960s in England, where water never gets that warm, nobody wore open-heel fins, everybody used full-foots, which were more expensive. For open-water use, we purchased full-foots that were one or two sizes bigger to accommodate thermal protection. Cressi even brought out "Uni Fins" in size 50-52, something like US size 16-20, to serve divers using Unisuit drysuits with their thick boots:
www.sukellusmuseo.fi
I only snorkel now, but I continue to wear full-foot fins, which I find both comfortable and appropriate for my gentle style of swimming, in the cold North Sea. If possible, let your daughter try both open-heels and full-foots and come to her own conclusion about what is most appropriate for her when she goes diving. I certainly wouldn't just take the word of somebody on the telephone who has probably either been told what to say or is simply pushing open-heels because they're the flavour of the century. Don't let somebody else make up your mind for you when it comes to gear. The purchaser is the one who's diving with the gear, not the salesperson.