science

Their classification is usually composed of one or more of the following properties

1structures(how they were emplaced in an energy system
2formative means (igneous sedimentary metamorphic)
3physical properties (for geotechnics)
4Chemical properties and crystal properties (for their chemical makeup)
5depth of emplacement(used for calorimetry and "geothermometry")
6global tectonics (are they part of a geosyncline, flysch, shield etc)
7paleomagnetics(defined by magnetic "chrons")
8Age
9AASHTO-(a building and aggregate class)
10 cement quality(unique only for low Mg cement stone)
11 Sedimentary Formations (the formal formation name is based upon a "type section" for sedimentary or metamorphosed sediments and certain metaigneous rocks only)

There may be some other minor classifications (like evry archeological material is classed according to a lithic source , like spear points are made of cherts,cryptoquartzes, rhyolites, or "hardstones")

There's hard rocks like diamonds.

And there's less hard rocks like volcanic basalt.

And there's even less hard rocks like granite.

There's a long series of rocks.

None of them, not even the softest, are worth banging your head up against. Especially the diamonds.