It is indeed the same experimental setup. There are three differences.The first is that the MM experiment assumed that the equipment was a fixed shape, and was looking for changes in the speed of light, whereas LIGO assumes the speed of light is constant and is looking for changes in the shape of the equipment caused by passing gravitational waves.The second is that LIGO is hugely more sensitive. By many orders of magnitude. Which is why there have to be two versions thousands of miles apart so that if some local event, from an experimenter dropping a book to a small earthquake, creates a bogus signal at one, it can be contradicted by the other.Third, of course, is that LIGO has generated a positive, to everyone's delight, whereas the MM experiment generated a negative, to everyone's surprise.