If OP bets because he thinks he's ahead and wants worse hands to call, it's a value bet—regardless of whether he's betting when first to act, last to act, or somewhere in the middle.
If OP bets because he thinks he's behind and wants better hands to fold, it's a bluff—again, regardless of his position.
In this exact spot, I don't know whether OP is ahead or behind on the river. I think it's entirely possible that someone shows up with AK or QQ here. (In my $6/$12 games, not everyone caps the betting preflop with these hands—in fact, some players don't raise with them at all.) OP could also be up against a made flush or the K
with some kicker other than an Ace, or any KT. So I would check for pot control and try to get to showdown cheaply.
This is very player dependent, but checking when this scare card hits might also induce a worse hand to bluff (or value bet, in the case of an AT or QT that might now think he has the best hand). So I might say that I'm checking here for pot control and possibly to induce a bluff.
A similar situation arose twice in my last session, and I checked both times. The first time, my opponent bet, I called, and he showed the nut flush, which he had slow-played on the turn. The second time, my opponent checked behind me, I showed pocket Kings, and he showed A6 for a turned pair of Aces with a weak kicker. So my river check saved me one big bet.