What is the difference between limestone and marble?

Very little, chemically. Both are calcium carbonate.

The difference is what happened to them. Limestone settles and hardens. Marble is limestone that was buried much deeper, then heated and squeezed until the mineral recrystallised.

Under that pressure the shells and fossils are erased. The grains lock together into a dense, even stone that will take a polish.

So marble is not a different mineral. It is the same one, rearranged.

Worth knowing
Makrana in Rajasthan has produced marble for centuries, including the marble of the Taj Mahal. It is limestone that spent long enough underground to come back as something else.

Source: Geological Survey of India.