Does Your Public Self = Private Self?

This question might be a no brainer to many people. Or is it? Does what present to the world at large, i.e. our Midheaven or MC, congruent with who we are really are, deep inside, i.e. our Imum Coeli or IC?

I'm speculating a "yes" to the question if there's some sort of connection between our public and privates selves. In astrological parlance, if:

• there's planet(s) in the 4th and 10th and they connect by opposition
• Ruler of 4th is in the 10th. This suggests that the private self is full public view. Which means the private and public selves are not too far off from each other.
• Ruler of 10th is in the 4th. The public self is actually the private self. Or that the public self is hidden. In other words, there's not much of a public self - you end with only the private self which means the public self is the private self. 

But none of the above three conditions applies, I'm inclined towards the view that public self not equal to private self which seems reasonable enough. The way we behave and act at home and with my family is different from how we act at work, on the telly, etc.

Musings on a Sunday.