One difference.
For the individual the provision of x may be a life or death choice; you will pay the maximum given that choice.
For the gov't, x is a bulk good (life and death are not at issue); the gov't gets a better rate.

As a patient with complete kidney failure, I have seen how this plays out first-hand.
A drug I needed was $5,000 a pop if I bought it as a person; buying through blue cross the price magically drops to ~$50.
It is a rather dramatic example of "market power" at work.