I have created the weapon or maybe an ammo stand and a settler is assigned to it, but honestly I have no idea what I gain from it?

It is a place to sell your stuff, and buy other stuff. If that is of value to you or not...only you can say.

Thanks for the info. So it's no different than me going to see Arturo in Diamond City? I figured it was at least something that could gain me caps?

Stores earn you caps, which are deposited into the workbenches of your settlements. Over time, and with 20+ settlements, earnings can be substantial. The only way to see your total wealth is go to workbench build mode and try to build a store, and you will see your total caps next to the cost of the shop. If you have 30k caps in your inventory, don't be surprised if you have 90k total combined, which was what I found out.

General stores, food & drink stores, clothing stores, and medical stores also earn you happiness, but weapon and armor stores do not.

Thanks buddy.

Correct. On my first character I built a bunch of them in Sanctuary so I didn't have to go anywhere but home to sell off my loot.