Oh good grief. Here we go.......
The waxes are the backbone of lube, and I tend to think about them on a molecular level like I think of bullet alloy, there are many similarities to the structures, shear planes, grain size, etc. which determine how the substance behaves under pressure, at various temperatures, and at mach point five or five. The waxes can be selected and blended to a very specific purpose once you get an idea of what each does and what they can do in certain combinations with each other, and with other additives like oils and metal soaps.
Micro-crystalline wax is a heavily branch-chained, petroleum wax which is sticky, tacky, adds lots of stretch, flex, and featherability/smearability to the lube (mixed with the right oils, this = "glide"). If a narrow fraction, like any of the waxes it can have a moment where it's solid and then goes liquid right now. It's better blended to make a more gradual phase change. Due to being branched and forming a crystalline structure, it holds oils very well like a sponge, provided they aren't of opposite polarity like PAG oil. By itself in a lube it can make awful cold-shot flyers because it's too tacky when condensed in a cold bore.
Beeswax is a blend of various ester waxes and some hydrocarbons, and a lot of other stuff. It has a pretty broad phase shift, is tacky, flexible, flows well, has very high film strength when liquid, has lots of fine particles and glues in it which make fantastic stop-leak, and due to the ester content will blend with dang near any oily stuff or wax on the planet. Also due to the solventy nature of the esters and very clean burn characteristics, it tends to not leave much carbon fouling behind in the bore. One other point is Beeswax is close to the ideal wax (almost) because it's solid and liquid friction characteristics are close for the purposes of bullet lube.
Paraffin has limited, but distinct use at my house. Paraffin is pretty much inert, but also very weak since its structure has lots of long shear planes. It doesn't lube well by itself, which like all the paraffin group of oils and waxes is a good thing. Low film strength has its advantages, one being soft paraffins (oils) are excellent for softening or plasticizing a harder wax without making the lube too slippery. Mainly I use paraffin to temper the sticky, cold-start features of microwax and to an extent, beeswax. 10% is usually plenty. The other neat thing about paraffin is it tends to make a lube liquify quickly (or at least flow like a liquid) with pressure alone, very handy for low-pressure loadings or situations where the lube needs to flow quickly without the benefit of heat, as in COLD weather. A small addition of paraffin can cure cold-barrel syndrome, but can also ruin extreme hot weather performance if sodium soap isn't present to kind of hold it together. Paraffin will also reduce the tack of beeswax and microwax, a feature which is invaluable to getting lube to jettison in low-pressure loads.
IDK about palm wax. Soy wax is awesome for glide and adding a lot of film strength, very good for high pressure lube BUT it will turn to goose chit in any kind of heat and it's tough to control in a hot barrel. In a way it's TOO good, but as an additive it has its uses, as does castor wax.
BP lubes are a whole 'nuther story better told by someone else.
