Sorry, McGrath, I didn't really answer your last question. E, B, and G are still Em, no matter where you play them on the fingerboard. For a fairly simple example (and a nice sounding chord, first finger on the first string, seventh fret, second finger on the second string, eighth fret, and third finger on the third string, ninth fret -- and the sixth string open (don't play the fourth and fifth strings). Voila! Em. What you have is E, G, and B up the fingerboard, with a nice low E bass. A first position Dm slid up two frets with an open sixth string bass is also Em.
Classic guitarists notate this by putting little-bitty numbers by the notes. If a number is circled, that's the string you play, the number without the circle is the left hand finger you use. Partial bars are indicated by something like MC-III. The "MC" stands for something like "mezzo-capotasto" or something like that, and it can mean holding down anything from two to five strings with the first finger, but there's some indication of how many in notes you play. The "III" is the Roman numeral "3" and means the half-bar is on the third fret. A full bar at the third fret would be indicated by "C-III".
There I go again. You may already know all this.
And Burke, "perfect" is not a qualitative term in this context. Two notes or three notes depends on whether you want a precise definition or not. Some study of the physics of music and why certain intervals are called "perfect" or "minor" or "augmented" or whatever should clarify what's going on. I've studied this a lot, but I'm not prepared to write a textbook on the subject. There are a lot of good texts already out there.