Asklemmy

There's a few levels down from each of those that you can get the broad strokes of fairly easily.

For igneous, you can broadly break it down into extrusive vs intrusive. Basically, did the magma slowly solidify underground, resulting in large grains like in granite, or did it come out in the form of lava that cools rapidly into fine grained or even glassy structures like obsidian. Then there's the other axis of "how much silica is in there?" Really high silica content rocks are called "felsic" rocks. Granite is an example of a felsic intrusive rock, ryolite is an extrusive felsic rock; Basically the same minerals, but way smaller crystals. On the other end of the silica spectrum, there's "mafic" and ultramafic rocks that have less silica and more iron and magnesium. The main example of a mafic rock you might know of is basalt. You can find charts like this one that break things down that way.