The mounded nest that ants build out of dirt or sand is called an anthill. You can call a similar mound built by termites an anthill too.
While an anthill is a kind of nest, it is generally formed when ants dig underground colonies and deposit the extra soil in one spot. In this way, an anthill is more of a doorway to a whole series of tunnels and nests, although the anthill itself will sometimes also contain nests. In some cases, ants shape the anthill into a specific, deliberate shape.