Simultaneously a Tax and Not a Tax

There are several aspects of the Supreme Court's decision on the ACA that still perplex me.

What exactly is the difference between a tax and a fine?
Don't taxes have to be paid before they can be challenged?
Don't taxes have to begin in the House of Representatives?
What is the explanation for the Medicaid decision?

I find reading the direct opinions can be very illuminating.  For example, I read the Conservative bloc's opinion, and came away with the realization that really they made a very strong case that Congress believed the mandate was not a tax, but not such a strong case, that it Constitutionally wasn't a tax.

Today, I think I can answer the second question.

This issue is discussed by Chief Justice Roberts on page 11 of his opinion (17 of the pdf)

It seems the answer to why this is not a tax for the purposes of the Anti-Injunction Act but is a tax for Constitutional Purposes is that the Anti-Injunction Act was written by Congress.  So it applies only to things that Congress thinks is a tax.

It would be like if you and I had different definitions for the same thing, say a computer.  Then I said I will buy you a computer.  Do you expect what you consider a computer, or do you expect that I give you my version of a computer.

Since Congress passed the Anti-Injunction Act, and said taxes must be paid before they can be challenged.  Then they wrote the ACA which calls it a "penalty," so the Anti-Injunction Act doesn't apply to it.  I'll try to think of an analogy to make this clear.