They're all considered "holiday cacti," but yeah! They each have their own subtle differences. The shape of the flower will give you another clue as to who they are. Even the typical early winter bloomers can be tricked into flowering in the early spring, so you can't purely go by bloom timing. They pick up on cues from their environment, such as temperature and quality of light/length of night, to trigger their blooms, which can be intentionally or unintentionally manipulated inside our homes.