I visited a different shop today, and they have crates of different rocks below their fish tanks. Sure enough, they had different color dragon stones. I tapped them, they seemed solid....... then I walked away!
Metamorphic rocks, as the name suggests, are rocks that have been changed, usually by heat, (pressure alone can metamorphose rocks, but it is a lot less common). from a base rock type. Typically, the original structure of the rock is destroyed and minerals recrystallized. Sometimes, new minerals can appear in higher grade metamorphic rocks, garnets are a common example. Most metamorphic rocks are suitable for aquarium use.
Granite and Basalt are both igneous rock types. Granite is plutonic, generally coarse grained interlocking crystals, due to slow cooling. Granite is at the Silica-rich end of a sequence of rock types, it may, simply, consist of Quartz, Feldspar and Mica. Syenite, Gabbro etc. are other members of this group. Basalt can be intrusive, typically dark, fine grained, found in dykes etc. or extrusive in volcanic lava flows etc. Extremely fast cooling can produce glass like rocks, Obsidian for example. Igneous rocks are safe for aquarium use, but can have sharp edges if rough cut/broken pieces - worth bearing in mind.
... I could probably go on for hours about this stuff. I studied Geology at University.