The two wrestling styles mentioned in the crossword solutions are SUMO and Greco-Roman. SUMO is a traditional Japanese style of wrestling that dates back to the Edo period. It is characterized by its ritualized nature and the use of a circular ring. Greco-Roman wrestling is a form of amateur wrestling that is contested in the Olympic Games. It is based on ancient Greek and Roman wrestling techniques and involves two competitors attempting to gain control over their opponent by using holds and throws.