Although I am not a geologist, I have been geogicaly trained, and I fully agree with the class Acci has been giving here.
It also depends on whether you take a petrologist view, or a geomorphologist or general geologists view. A petrologist will likely use names like Tephrite, Basalt, Rhyolite, Andesite etc. to refer to solidified “lava”. I.e., he wil go down to the petrologic level in his description. A geomorphologist will talk about “lava flows”. Vulcanologists have their own set of esoteric names.
Referring to solidified lava: there is a typology based on the structural aspects of the solidified rock, the main categories of which are:
* Pahuhu or ‘ropy’ lava: a wrinkled, ropy surface. Name is Hawaiian
* Aa: a very ragged, sintered surface. Name is Hawaiian.
* block-lava: how surprising, consisting of a blocked surface.
* pillow lava: a mass of pillow like blocks, typical for under water extrusion