Quoted for good information!Beta = installs a few files into a new folder ([path to game directory]\Arma2\Expansion\beta\), can thus be easily deinstalled by just deleting this folder. Can only be used with the proper shortcut, which starts the beta executable and some extra files, but that means you are also able to play the non-beta version of your game by using the normal shortcut that doesn't start the beta. Brings only changes in the engine, not different textures or something like that. A Beta only increases the build number (the 5-digit one, e.g. 95208), not the game version (e.g. 1.62 or something), and thus is compatible with all other betas that bear the same game version. Betas are brought out in quite regular intervals. If you want to see what improvements the next official patch might bring, you can use them, but are not forced to. Often they improve the game a bit, sometimes it gets worse and you better reverse to an older beta until it's fixed (that's why it's called a beta and is not an officially released patch).
RC (release candidate) = works like (and is a testing version of) an official patch, i.e. overwrites a vast number of core game files and changing content, can bring new content like different models, maps, textures etc. But CANNOT be deinstalled so easily, you either have to reinstall the game from scratch or revert it to a backup you made before. Increases the version number, so is not compatible with servers or clients which don't use the same version. RCs usually only appear a short while before the next official patch. Using RCs is a bad idea if you just want to play, they are meant for dedicated people in the community who have the time and knowledge to help the developers.
Battle Eye support usually is added within a few hours after a new beta (or RC for that matter) is out, so you might want to wait that time before you use it to play.
Maybe someone should write a proper explanation in a sticky, obviously not only brand new players but also guys who are around for ten years are confused by the different patch types. Sure it may be over in a couple of days when the final 1.62 is done, but the mayhem will start all over next time with 1.63.