What constitutes a “win”?

Title kinda explains it all, basically now that I’m a few hundred hours into the game, it seems like (unless I’m just farming Greed runs as Azazel) my win streak almost never exists. What specific bosses do you need to beat in order for a run to count as a win? I don’t have access to Mother or to the Ascension yet, but do I really have to go all the way to Blue Baby/The Lamb every time to count it as a win? I feel like if I manage to beat Isaac or Satan it counts TO ME but my streak disagrees