With Price, they trust his ridiculous cap hit will protect him. This lets them also protect Jake Allen, who many experts expected to go to Seattle, to maintain what was a pretty successful tandem.
Ovechkin is a UFA. Which means even if Seattle takes him, all they get is his negotiating rights until free agency opens up, at which point Ovi is free to re-sign in Washington. Seattle is allowed to negotiate with UFAs over the next few days, to see if they're interested in signing, before they pick a guy off a roster.
It's likely some will get picked, even to get flipped for rights reasons after. But Ovi? Nah, he's one of those guys that if he wants to go to Seattle, he'll tell them. And he doesn't, he wants to stay in Washington.