The aliphatic part of the name in the aliphatic resin is not the actual base of the glue, just an additive in it.

PVA/white glue is a PVA ( polyvinyl acetate), based glue, most aren't pure PVA , the pva is copolymerised with various other monomers such as acrylates, styrene, pva, eva etc depending on the exact type and level of various comonomers the glue will have different properties

Aliphatic resin is a PVA based glue (pva copolymer, as above) with an amount of an aliphatic hydrocarbon resin added as a tackifying resin , makes it more tacky at room temp when wet, not as rubbery so will sand better than a standard type pva glue

Then you can get aliphatic PVA , these again are an aliphatic resin added to a PVA copolymer, difference is that they are made with a colourless aliphatic resin to make them look like a white glue

All types of PVA or aliphatic resin can have many other aditives to alter the speed of set and wether they crosslink after drying to make them fully water resistant or not