What's the difference between "I must help her" and " I have to help her"
Solution 1:
they say that 'must' is more for personal obligations.
That is not true; when somebody says "you must show your ID card," it is referring to an external obligation (e.g. by a law) not to an obligation you personally have because your ideas.
Solution 2:
Mmmm, that's a subtle distinction that I think the website is inventing or imagining. To my ear, "must" is simply more formal.