What is the difference between "If I must" and "If I had to"?

Solution 1:

The difference is seen in the following clause in each sentence. Take these examples:

If I must leave my employer, I shall bring the company down.
If I had to leave my employer, I would bring the company down.

The first is looking a distinct possibility, even probable; while the second is merely hypothetical and may not happen at all.

Solution 2:

Let me answer by example:

If I read "If I must go out in the rain, I will bring my umbrella" I would understand that the person does have to go out into the rain, and is telling me that they're about to go get their umbrella because they're about to go out in the rain.

If I read "If I had to go out in the rain, I would bring my umbrella" I would understand that the person is expressing a preference about a hypothetical situation. They don't have to go out in the rain at this time, but if they did, then they would want to get their umbrella.

In the first one, the going out in the rain has already been decided. In the second, the going out in the rain is not an immediate concern, but a situation that the person is prepared for.