And is correct that way because inputs "... are always lowercase strings, and that each has at least two letters.". If that was not the case and arbitrary inputs would be allowed we'd also need checks for null and lengths in order to avoid NullPointerException and IndexOutOfBoundsException or alike.

it work only if cases are equal

I would rather have more spaces to increase the readability of the code, but it's okay

Not true. If n or m are 0, first if will be true, and return 0

Very efficient

If n or m are 0 you will return -1. Why test didn't check that?

If n<0 and m<0 your code will not see an error, but I understand, that there won't be negative input.