Molten rock is called  magma when it is beneath the earth  .
Crystals of minerals form in the cooling magma. Because the cooling magma is insulated by a blanket of earth, it takes a long time to solidify (harden). This long cooling time allows the crystals to grow quite large. 
Rocks formed from cooled magma are called intrusive or plutonic*  igneous rocks. Granite is a good example.

Molten rock is called  lava when it is above the earth .
Lava cools quickly, and so any crystals that form are small. 
Rocks formed from cooled lava are called extrusive or volcanic  igneous rocks. Basalt is a good example.
Geoscience Australia has information on volcanos.