yeah. it's different in later games, but wots1 saving is just saving your position in the story, like pausing your game even with the system off. If you played the Castlevania games on the GBA, it's like the sleep save option.
It's no big deal because the games are short. Like Dead Rising, it is a game about learning and replaying. You don't have a leveling up system for your character but you can collect better swords that get saved, and you unlock more character customization options. Later games have more things that carry over between games. The big thing about the new WOTS4 is that they're adding more when you replay the game. I forgot to mention that.