Kind of. In the UK we only refer to the minced, salted and then tinned beef as corned beef. If it's not tinned, then we would call it 'salt beef'. In the US both the tinned and non-tinned varieties would be called 'corned beef'. So, if you find a corned beef hash on the menu in America, what you'll likely get is a plate of salt beef mixed in with potatoes.
I have to say though, salt beef looks an awful lot better than tinned corned beef. Making this dish look appetising may be one of the biggest challenges I've had on this blog!
Another thing to bear in mind is that, in the US, corned beef is associated with Irish cuisine and is often served on St Patrick's day. In reality, it is simply not a popular ingredient in Ireland. Ireland's relationship with corned beef is actually because it historically farmed a lot of cattle to export beef to mainland Britain.