Different Christian traditions emphasize one or the other, but all acknowledge that both types of sin exist. Sinful actions come as a consequence of this state, but one could be in it without having yet committed any actual sinful actions. Original sin is an explanation of why we are in this state of sin. Total depravity is the doctrine that all of our nature is corrupted by sin. From time to time people have tried to trace sin to ignorance, to sex, or to other specific human faculties.
Total depravity asserts that our entire being is involved in sin.
Sin is not just a matter of not understanding something. It is basically a derangement of the will, so that we are focussed on ourselves rather than God. Similarly, it shows up in everything we do. This does not mean that everyone spends all their time in rape and pillage. People are capable of good actions.