I probably couldnt tell you anything about either except that both can go in water. So, whats the difference? or the same?
Besides one of the most obvious differences mentioned above (inner lining & drawstring) boardshorts are usually designed with a more durable material. Being that they are intended for surfing which is a pretty physically demading sport, a high strength nylon material is used. They are also designed to withstand the abuse of the natural terrain that occurs depending on where your break is. These include corral, rocks, rough sand, etc. Most times, a standard bathing suit is made of a more flimsy material that is a little more comfortable to wear. Basically, boardshorts are designed for performance and bathing suits are designed for leisure/comfort.
I assume you mean mens shorts.
The Swim Trunks are softer and have a mesh lining like underwear. They usually have an elastic waist with a drawstring to tighten them.
The Board Shorts are heavier so you don't get scraped when you rub against the surfboard or the sand. They usually have a velcro fly with laces to tighten. Not an elastic waist like the swim trunks.