Heres a video on how to wear a sarong, notice how unlike a towel or bedsheet its not a rectangular piece of cloth. Its as if two opposing ends of a towel were joined, turning it into a tube of cloth.

Its worn casually in some and formally (traditional clothing) in others, the material and design can get very elaborate. Its worn by men and women in lots of different ways.

Im speaking from experineces in south and south-east asia, it might be different elsewhere.

I don't have experience with a sarong, but a saree is basically the same thing.

The difference is in the shape and size of the piece of cloth. That's how you can tell a saree, bedsheet and towel apart. There is also usually difference in material (but fine silk towels exist, as do coarse cotton sarees), patterns/weaves (but there are towels and sarees that share pretty similar patterns) and quality of materials used (but again, ridiculously high quality silk bedsheets are a thing). The real difference is the shape and size - sarees are always 5.5m x 1.15 m ('standard' 6-yards), or 8.2m x 1.15m (9-yards, worn only on special occasions now, and only in a few specific regions).

In a pinch, a saree works as a towel or a bed sheet or a cover sheet of any sort, really. However, good luck getting a towel or bedsheet draped onto your body - you'll look like you're in a sack. They just don't have the right shape!

It’s similar to the difference between toilet paper and facial tissues. Size, texture, materials, thickness… etc.