Android : phones give off signals that can communicate between each other

Do smart phones give off signals that can communicate between each other that are accessible via an app ? Is it possible for a smart phone to exchange information with another phone by tapping it? For example, two people touch their phones together and the phone gyroscope picks up the tap and the two phones exchange information if they are running the app. This can work if one user has an iPhone and the other user has an android?

Also, is it possible to have an app that knows when other users have that app if they are in the same room?

If you have any experience please guide me and suggest and it been appriciable.