The two terms specify the nature of the procession that occurs between the persons of the Trinity. Generation is the procession of the Son from the Father, whilst spiration (n1) is the procession of the Holy Spirit from the Father and the Son (n2).
n1: Spiration is derived from Latin spirare “to breathe”. “Spirit” and “breath” are denoted by the same word in Hebrew, and this semantic relationship was bequeathed to Greek and Latin theological terminology.
n2: Within the Eastern Church, spiration is understood to only occur between the Father and the Holy Spirit (cf the Flioique dispute).
Of course, there’s much more to procession in the Trinity than what I’ve written, but this is a modestly simple and accurate summary.