I say the JD ones are "fakes", because they are blatantly ripping off Bandai. Other virtual pets like dinkie pets, nano pets, giga pets, etc. aren't fakes, because they are their own brand. It's just like another company making an item similar to something that already exists, but not completely imitating them.
A perfect example of making something similar to an original item: I've worked in several different coffee house chains and people would come in and ask for a "frappuccino". And all of you know Starbuck's owns the rights to that word, etc. A frappuccino is just a fancy name for a ice blended drink and most coffee shops offer an ice blended drink. it doesn't mean their drink is a "fake" frappuccino, that would be absurd.
These virtual pets are basically the same thing.