Essentially hay is hay, but some varieties like timothy are more expensive to grow, and hence you'd only want to use them for feeding rather than bedding - plus they tend to be stalkier so nicer for chewing and a good source of fibre than they are for sitting on. Some hay listed as bedding hay has been chopped up into small, even sized strands, so it is more convenient and comfortable for use as bedding, but there's no reason why bunnies couldn't eat it.