You don't have to memorize the fretboard, but you should at least memorize all the notes on the 6th string

You can play everything from this string, either scales - minor or major or chords - minor or major using barre chords or power chords. That will cover a lot of songs or jams.

You should also learn the major pentatonic scale pattern and the minor from this string as well if you don't already know them. 

And the key means root. So key of C means the chords will be in the key of C - either major or minor and so will the scales - major or minor.

If you want to know what belongs to each and don't want to memorize the formulas, go to this link below.

Keys

Edit:

I am going to add a bit to this, not knowing how deep you want to go into this, but there are times when a "note" is not a "note". Example, you may be learning a song and a lick has the following notes: E E C# / D D C A.  You can find those notes anywhere on the fretboard, however, if you aren't playing the EE's on the 5th fret of the 2nd string, it won't sound correct to the song.

So when I am learning song parts I try to figure out where on the neck the parts are being played.