The most popular are short jean shorts, they are all-rounders and are the most worn trousers in the world.
Also like the jeans shorts, the short chinos = light cotton trousers are very popular.
Bermudas are made of many different materials as well as jeans or chinos.
Cargo shorts, originally trousers for workers, have patch or sewn-in pockets on the side of the thigh or at the knee. They have become a major trend this year and are very popular with young people. Cargo means freight.
Then there are the sweatshorts, they look sporty, have a drawstring, are made of soft fabric and are super comfortable. They can be worn with a long-sleeved shirt, hooded jumper or cardigan.