How do government and the private sector intersect? How should it?

I had a difficult time with this question.  I guess I don’t fully understand what a public sector or private sector truly consists of.  Ultimately, the money we make goes to the government right?  Whether it is taxes from income, property tax or even sales tax, the government gets a good portion of what we earn in wages.  Interestingly enough, in a way we are in charge of our government.  Through our voting privileges, we can elect who is in office at a particular time.  So while the government seems to hold a certain amount of control over the private sector, does the intersection take place by setting them in a higher pay scale?  Is there an interaction that government workers will make more because private sector employees in privately owned business make less?  Or is it just coincidence?  Maybe the two should interact in a more productive way.  If the government can regulate certain aspects in the private sector, then why don’t they do so in a way that will earn the private sector more money?  If this is the case, both sides can economically be satisfied.   Also, if the government is relying on private sectors’ tax money, then shouldn’t it be less given the fact that they are already in a safer more controlled environment?  I feel as though jobs on the government side seem more secure as where the unemployment rates in the private sector seem to fluctuate substantially over certain periods of time.

Again, I wasn’t 100% clear on the question being asked, but from my take, we were supposed to give our reasoning as to how it should intersect, which means aside from the way it currently does.