If they are Petroleum Oil based,,they will usually have Mineral Oil in them as that is the most common highly refined Petro Oil there is.
There are many grades of mineral oil for specialized uses.
Rem-Oil uses it along with mineral spirits and some other additives. Some are petro, some are synthetic.
CLP is all synthetic,,no Mineral oil or Petro oil at all.
Ballistol is Mineral oil (medicine grade) , alchohol, Oleic Acid (alkaline salts,,likely from Sodium ), and that love it or hate it smell from
Anise or Aniseed extract. .
Some others use Teflon and other additive ingredients.
Marketing claims are all over the map. Every one of them is the very best there is of course.
One will prove to be the best choice for an individual after some experimentation. But everyone will usually come to a different conclusion.
Just like what's the best patch lube.