intarsia is a word that comes from italian, it means 'an inset tile'
intarsia is inset color work (like a tile) a pattern that is inserted into a solid background of knitting..
Though it can also be used for multi colored mosaic tile like all over patterns.
Fair Isle (note caps!) is a style of color work associated with Fair Isle (one of the small island off the coast of scotland)
fair isle (no caps) is a term used for any sort of color work that is done in rows..
as a general rule, fail isle (with or with out caps!) is color work that uses 2 colors per row, (but there might be 6 or 8 or more colors in a design (2 rows of A & B, 2 rows of B &C, 2 rows of D & E, etc)
there are several "rules' for true Fair Ilse, (note caps) but the term fair isle is also used for lots of different kinds of all over color work.
Intarsia is difficult to work in the round...(it can be done,but not easily)
Its not uncommon for socks like yours to be knit flat (and to use intarsia) for 'leg' and to be joined into round for heel/foot/toe.