Magma is the term for any molten silicate material, whether below the surface or on top.
Magma that is injected and crystallized below the surface forms intrusive igneous rocks. Because they cool more slowly than extrusive rocks, intrusive igneous rocks are generally coarse-grained (>1mm). A very coarse-grained igneous rock (>2cm) is called a pegmatite.
The same compositional variation seen in extrusive rocks is seen in intrusive rocks, but the rocks are given different names:
Extrusive Intrusive Composition
none Lherzolite Ultramafic Basalt Gabbro Mafic Andesite Diorite Intermediate Rhyolite Granite Felsic
Ultramafic rocks are almost entirely ferro-magnesian minerals. Ultramafic extrusive rocks are very rare and most ultramafic rocks are the residue of partial melting.
Mafic rocks contain roughly equal amounts of ferro-magnesian minerals and calcic feldspar.
Intermediate rocks may contain minor quartz 20 to 30% ferromagnesian minerals and intermediate (Na-Ca) plagioclase feldspar.
Felsic rocks contain minor ferromagnesian minerals, abundant quartz and both Na and K feldspars.
Igneous rock compositions change as the result of partial melting and fractional crystallization. This is illustrated on "Bowens Reaction Series".
Mafic magmas are typically hotter than felsic magmas. Dissolved water greatly lowers the melting point of any magma so that a saturated felsic magma may be as low as 800 º C, whereas a dry mafic magma may be as hot as 1250 º C.
The shapes of igneous bodies also have specific names:

Here a basaltic dike intrudes precambriam sediments at Hance Rapid in the Grand Canyon, Arizona, USA.