Concise Bible Dictionary:
The word εὐσέβεια,—βέω, signifies “to exercise piety, reverence”: a reverential sense of having to say to God, which should be shown by the creature to the Creator, and which should especially characterize the saints towards God their Father and to the Lord Jesus. The word is translated “piety” in the AV only in 1 Timothy 5:4. It is rendered “holiness” in Acts 3:12 and “worship” in Acts 17:23. In all other places it is “godliness.” “Piety” is a better translation, and distinguishes it from θεοσέβεια, which signifies “worship, or fear of God,” and is translated “godliness” in 1 Timothy 2:10.