Good answers here. Just to add to the conversation, if someone says “He’s out of his depths”, the meaning is the same as being in over one’s head and _not_ being in too deep (even though deep and depths come from the root). I don’t mean to muddy the waters, but I wanted to addresss what I thought could be another, similar, point of confusion. Victor

Hi Tiger, They are not exactly the same; they are more or less synonymous. Cambridge Dictionary: "1) be in over your head informal to be involved in a difficult situation that you cannot get out of: Sean tried to pay his gambling debts, but he was in over his head. 2) in too deep too involved in a difficult situation NOT to be confused with: 3) over your head too difficult for someone to understand: Most of that lecture was over my head. I tried to take in what he was saying about nuclear fusion, but most of it went over my head."

They are similar, but not quite the same. You're in over your head - you are involved in something beyond your capabilities and you need help. You're in too deep - in a difficult situation that one cannot get out of

In short, yes.