"Acting out" is a potentially useful term which has been inappropriately objectified. It is the beginning of a phrase, or rather it is the beginning of a collection of phrases such as acting out frustration or acting out anger or acting out emotional dissonance. The point of this collection of phrases is this: When people are unable to verbalize their experience, acting may become the dominant method of communication.
There is a tendency to take the two common words at the beginning of these phrases and objectify them as if "acting out" were a thing in itself, separated from the true object -- the frustration, the anger, the dissonance, the pain. Or the joy, the pleasure, the love, or whatever else is the objective reality which underlies the acting. This tendency to objectify the two common words is partly mere shorthand, which is convenient if the full underlying reality is not forgotten, and partly an expression of our human need to group and categorize, which recognizes the similarity of all types of "acting out".
There is nothing wrong with shorthand or with categorization, provided that the reality which lies behind them is not lost. A person who is "acting out" is always acting something out. The acting itself is not the problem, but that something may be a problem. Objectifying the phrase "acting out" can limit our attention to the mode of communication, the acting, and in that way can become a barrier to seeing the content of the communication.
But seeing the content may be the one thing no one wants to do. If the content being communicated is painful, frustrating, dissonant -- if that is the experience which is being acted out, then protecting yourself from that content is natural.
In actual reality we all act out our thoughts and emotions. Our language-based culture means that verbalization often dominaties our communication, but words do not negate behavioral modalities which can range from hand gestures through tone and volume modulation of our voice to our choices about when to be present or absent for specific activities. All is acting.
When we experience life as being harmonious we act harmoniously. This seldom attracts much attention.
When we experience life as inharmonious, we act out conflict. When we experience life as painful, we act out pain. More than just words, and especially when words fail us, our acting transfers some of the dissonance and pain to those around us. That is very often noticed.
Thus "acting out" often successfully communicates the reality of our personal experience of life to other people near at hand. People near at hand are very likely to respond by wondering, "Why are you communicating pain and dissonance to me? I don't want your pain and your frustration and your anger." This is a reasonable and normal response. But what comes next? Is it, "Let's try to eliminate the reality which you are experiencing"? Or is it, "Stop communicating your life to me"?