The method of production of sea salt usually involves bulk evaporation of seawater. This allows the salt to crystallise and due to it's bigger size it is sold without much processing. On the other hand, the table salt has much smaller size and is processed a lot more than we could assume before it is sold.
This could be one reason why sea salt has coarse texture.
See also: Maxine Builder and Maxine Builder. What's the Difference Between Kosher Salt and Sea Salt? (via the Internet Archive)
I was interested to answer this question because I have always thought that both the salts are just the same. The tiny size of salt grains just seems less coarse but it essentially is having the same texture is what I would believe.
But then I looked at sugar as well. The tiny grains of sugar or a little bigger sugar diamonds seem smooth compared to the rough textured bigger blocks of sugar. And so I was convinced that it was due to it being processed. But then think of powdered sugar? That appears to be smooth.