Erasers can be made of either rubber or vinyl. Rubber erasers tend to degrade after a while (oxidation?) and may also be heir to problems directly attributable to the quality of the rubber. Vinyl erasers (the white kind) tend to stay softer, clean easier, and erase better. I’ve found that they wear out a little faster and make more “crumbs”.
As for pencil leads, it’s all graphite with some clay mixed in for hardness. 100% graphite will give you a very dark, very soft lead that will lose its point very quickly. The more clay you mix in, the harder the point, but clay being cheaper than graphite, some manufacturers will cheap out and produce a point that’s more clay than graphite, which is brittle and won’t stand up to regular use or sharpening.