Sober means free of alcohol. Clean means free of other funky chemicals. If you're sober but not clean, great, but it won't get you far. Vice versa: true also.
But there is no such thing as 'emotional sobriety'.
'That's not very sober!' is something people they say when they would like to condemn someone else's behaviour. All it means is 'I don't like what they did.' It does not mean the person is drunk or that their actual sobriety is somehow lost or compromised.
Sometimes people say they're not emotionally sober when they're actually experiencing perfectly ordinary human emotions in response to a genuinely challenging situation.
Using 'sobriety' to mean something other than sobriety is a dual-victim crime. First of all, it equates, say, a tantrum with someone drinking, which, if they are an alcoholic, could literally kill them. Very few instances of 'emotional inebriation' come close to what can happen to an alcoholic who resumes drinking. This trivialises alcoholism and diverts AA from its primary purpose.
Secondly, it does not describe the emotional state or behaviour. Let's call things what they are. Immorality. Breach of etiquette. Selfishness. Immaturity. Pig-headedness. Incompetence. Overreaction. Childishness. Touchiness. Cowardice. Self-absorption. Take your pick! If you can name it accurately, you have a much better chance of doing something effective about it.