Rosti and hash browns are just about the same thing and made of the same ingredients which is shredded potatoes.
The only real difference between Rosti and hash browns is that one is thicker than the other and the other is thinner.
Hash Browns are thinner while Rosti is thicker than the hash browns.
Other than that there's not much of a difference betwene the Rosti and hash browns other than the thickness and the name.
Essentially when you're making or eating the Rosti and hash browns you're eating or making the same food.
Some people also like to serve Rosti with eggs which makes them even better.