Gregory freely admits that ungenerate is simply a way to say Father (Against Eunomius 1.37) He prefers the revealed terms of Father, Son, and Spirit to any systematic terms like ungenerate and generate, but he understands the necessity of the latter given the heresies of his day.
He is concerned with guarding the eternality and uncreatedness of the Son, however, and so he grants this admission when it comes to the use of “generate”:
In our view, the ‘native dignity’ of God consists in godhead itself, wisdom, power, goodness, judgment, justice, strength, mercy, truth, creativeness, domination, invisibility, everlastingness, and every other quality named in the inspired writings to magnify his glory; and we affirm that every one of them is properly and inalienably found in the Son, recognizing difference only in respect of unoriginateness; and even that we do not exclude the Son from, according to all its meanings. But let no carping critic attack this statement as if we were attempting to exhibit the Very Son as ungenerate; for we hold that one who maintains that is no less impious than an Anomoean. But since the meanings of ‘origin’ are various, and suggest many ideas, there are some of them in which the title ‘unoriginate’ is not inapplicable to the Son. When, for instance, this word has the meaning of ‘deriving existence from no cause whatever,’ then we confess that it is peculiar to the Father; but when the question is about ‘origin’ in its other meanings (since any creature or time or order has an origin), then we attribute the being superior to origin to the Son as well, and we believe that that whereby all thins were made is beyond the origin of creation, and the idea of time, and the sequence of order. So He, Who on the ground of His subsistence is not without an origin, possessed in every other view an undoubted unoriginatedness; and while the Father is unoriginate and Ungenerate, the Son is unoriginate in the way we have said, though not ungenerate.
~ Against Eunomius 1.33
Notice that the Son is without origin when it comes to our concept of time and coming into being. The Son is superior to all such concepts of origin. His generation from the Father is purely within the transcendent and simple essence. When it comes to relations with the creation, the Son is without origin. When it comes to the relations within the godhead, His cause is the Father’s own essence, which is His own essence as well.