I suppose you can put different terminology on it - and that might be appropriate, dunno - the context is clearly different, but the body language of a dog stalking up to another dog says to me 'if you run, I'm going to chase you down' - and that is what makes the dog on the receiving end of the behaviour freeze (or react defensively). So it sort of looks the same to me, the intent toward prey is also clearly aggressive eg a desire to kill it.
Brogan would do the stalking with me, it was one of our regular ways to play. I always loved it and could get him going every time. He'd pretend to stalk me, I'd do it back to him, and the one who "broke" first was the loser with the winner running around like crazy (yeah, Brogan was usually the winner as he had a lot more patience than I do!).