I remember one of the first apps I downloaded on my iPod Touch in middle school (~2011) was a "binaural audio" app that catalogued spatial audio experiences (+ voice-acted stuff like getting a haircut, etc).
Spatial audio is a more generalized term. Let's say you're filming an action movie and have a scene where a robot comes from foreground-right, kicks a car, and the car flies over the camera and makes a loud crashing sound behind the camera. You can't just stick a binaural microphone on set and record that because it's almost all CGI. There is no actual sound of a robot kicking a car to be recorded. Instead your foley artists and sound design team will record and modify dozens (even hundreds) of sound sources and combine them together in software that supports a sort of virtual 3d environment, and save it in a format capable of representing this (like Dolby Atmos).
You can then take that Dolby Atmos data and in realtime compute how to map your virtual sound-sources onto things like a 64-speaker Dolby Atmos array in an movie theater, or a 12-speaker home theater Dolby Atmos setup, or apply an HRTF to convincingly map that audio to 2 headphones. A Binaural audio signal is restricted to stereo and intended to be placed directly in the ears.