Barr chords

artic fox,
Yes you move the shape up (toward the hole).
You have your regular E, barre F - move up one more gives you F#, one more up is G, up one to G# (Ab) and so forth.

the other question you asked "what makes it an F in the first place" is another part of basic music theory its easy to get lost understanding and sometimes trying to explain you have to take it a little at a time to really let it sink in but to start with a major chord is made up of three notes in the key: a F major scale uses the notes F G A Bb C D E F the reason the B is a Bb is because of the intervals in a major scale,if we use the C scale its easier to understand this formula 1 1 1/2 1 1 1 1/2 or whole whole half whole whole whole half each major key is laid out the same way now a simple C chord has the notes CEG the reason being a major triad is the Root (C) the 3rd (E) and the 5th (G) or 1 3 5 this is a C major chord  thats enough for now learn this much and you can use this formula later to figure out the notes in any scale and to constuct major chords, minor chords are 1 b3 5 or C Eb G like I said its a lot to learn but you have to start somewhere

Good question, brilliant replies, back in the dark days of the last centuary (you know about the time when England was last winning the world cup!) mum and dad gave me a guitar and a school teacher was kind enough to give up his lunch breaks to try and teach me some songs using chords.  Our family moved and I dropped out of guitar playing after a few years, never having progressed much. A couple of years ago I took it up again and a performer at our local pub said "learn barre chords its worth it in the long run" A few false starts and wow was he right.
Someone on Chordie, to my shame I can't remember who, was good enough to mail me a chart with all the finger positions for each type of note (major, minor, 7ths etc, etc, working off the root note (the position on the 5th or 6th string)  for barre chords, its been invaluable to me so I will pass it on to you vie e-mail as i dont know if I would be allowed to post it here or even how I could post it here! Hope it will be of assistance. Stick with it when you start getting the hang of it and they start sounding right it all suddenly makes sense!