Both petroleum-based and synthetic cleaners use a base oil that is obtained from petroleum. Cleaners made from plants employ plant-derived oil that is extracted from specific plants and purified to a useful state. Similar to how olive oil is produced, the flavor of plant-based gun cleaning solutions when combined with balsamic vinegar isn't quite as good.
CLP made from plants is typically non-toxic as well. It depends on you if you think that should be a priority.
In general, there are three types of gun clp. To expand on it a little, there is a base component that is combined with a variety of surfactants (chemicals that dissolve deposits on a surface). One of three categories can be used to group gun-cleaning compounds:
Petroleum \sSynthetic \sPlant-based