I don't think it matters which you use.     Straw is the stalks of wheat or barley or whatever grain  they grow around there, with the seed heads removed. People buy it for animal bedding, mulching gardens, etc.   Hay is other types  grasses cut and dried, seeds and all, and it's used for feeding livestock.   There are lots of kinds of hay available, fescue, timothy, orchard grass, bermuda, clover, alfalfa, native grasses, etc , each will smell different, have different nutritional qualities..    Any kind of straw or hay can get moldy.  I'd say, use what you like best.