Rosaries can be made with any kind of materials, as long as they have some form of bead or beadlike object (no matter what it’s made of, or the shape), and don’t even have to have a crucifix on them, in fact. The centerpiece medal, likewise (if you even have one) can be anything.
So like some others said, some people like to make or buy rosaries with a symbol in the centerpiece that serves to honor or remind of the first communion or rosary - i.e. a chalice and host symbol, or holy spirit, etc.
It’s not an actual different kind of rosary.