You may hear the word "key" used in much the same way as "scale". A key is another word for a selected group of notes out of the octave. The word scale is used more often to refer to the act of playing all the notes, while the word key just refers to the group as a whole.
Every scale, or key, has a "root". This is the note that the scale starts and ends on, and the one it is named for. For example, the root of a B major scale is B. Usually, you can hear which note this is. It will sound like the "home" or "base" of the scale. With a little practice, and sometimes with none, you can hum the root of a scale you hear, even if it didn't start in the right place. In much the same way, you can also probably pick out the root of the key of a song you're listening to.
The difference between a "right" note and a "wrong" note is basically whether or not it is a member of the key you're in. If you are playing a song in the key of C major, you probably shouldn't play any note that isn't in a C major scale. Learning your scales is how you learn to avoid wrong notes and play things that fit in well with the rest of the music.