Of course we do need to make the distinction. There is “good” in the human standard, which is governed by our reason. In that sense, one can say one is “good” if he lives a life consistent with what a reasonable human being would expect from one who ought to live a life in peace with fellow human beings.I do think that an atheist can be good, but not without God. What I mean is that the law is written into our hearts. To the extent that the atheist follows God’s law, they are a ‘good’ person. However, it is God that writes the law on their hearts and moves them to understand it.
But there is also “good” in the theological sense, and here, Jesus’ words come into play: there is none good but God alone (cf. Mark 10:18). Which is right, because man is now fallen; we are born into original sin, and nothing unclean enters heaven. This is why Christ came, died, rose, and left us the Sacraments, especially of baptism and penance, so that we can enter and be restored to his grace, because by ourselves, we are not “good.” To enter heaven, we need to have in us the goodness of God himself, not our own. In this sense, good and holy are equivalent.