Greedy sorts are algorithms that prioritize efficiency over other considerations. The two most common greedy sorts are PIGS and HOGS, both of which are four letter words. PIGS is an acronym for 'Picking the Greatest Element Repeatedly', while HOGS stands for 'Heuristic Optimization Greedy Search'. Both algorithms work by selecting the best option available at each step, without considering the long-term consequences of their decisions. This often leads to a solution that is not optimal, but is still relatively efficient.