Concise Bible Dictionary:

Besides the word πρόσφατος, for the newly-made and living way in Hebrews 10:20; and the word ἄγναφος for the new (unfulled, unfinished) cloth in Matthew 9:16 and Mark 2:21; there are two words translated “new,” the difference between which is important. One is καινός, “new” in the sense of never having existed or been used before, that is, new in the sense of “different”; and νέος “new” in the sense of “fresh, youthful.” The new (νέοσ) wine must be put into new (καινός) bottles (Matt. 9:17). Except in the Gospels, in reference to the wine as above, the word νέος is used only in “a new lump” (1 Cor. 5:7), “the new [man]” (Col. 3:10), “the new covenant” (Heb. 12:24), and “young woman” (Titus 2:4). In all other places the word employed is καινός, and this is important, as indicating the entirely different character of the new covenant, the new creation, the new man, the new heavens and the new earth, from all that had been. “He that sat upon the throne said, Behold I make all things new” (Rev. 21:5).