I have heard generally that it is possible to put different physical theories on a lattice and after renormalization get the same continuum theory. I mean, different lattice theories that lead to the same continuum theory. Is this true for, say, qcd, or other particle theories? Are there different varieties of lattice qcd that give the same continuum qcd theory? And if so, is it known how these lattice theories are related, besides their obvious shared macroscopic limit? Thanks.