A formal term for overcoming something, or getting over something I am trying to find a correct psychological term for a specific type of behavior.

When a person is trying to distance themselves from past suffering by projecting an idea of "I'm over it" to others. Trying to convince others and maybe even themselves that they've overcome something.

For example, a person who has suffered depression is trying to project an idea of "I'm over it and never going back" to another person suffering from depression.

A similar example would be about two people dealing with divorce or breakup and one person tries to project that they are over it not wanting to feel the pain or suffering that the other person is experiencing.

Is it distancing? Is it disengagement?
Since there are different types of distancing, some positive some negative, what type is this?
Is it overcompensating?
Or something else completely?
The term you are looking for is probably dissociation. 

There is a range or continuum of experiences that can be subsumed under "dissociation", going from mild to pathological. On the pathological end of the continuum, for example, there is dissociative identity disorder. 

Dissociation is technically a kind of defence mechanism. See for example the article Dissociation Isn't a Life Skill on Psychology Today. The International Society for the Study of Trauma and Dissociation has a long list of Dissociation FAQs.