"power chords"

I've two different questions in regards to "power chords"

1 - what's the difference between "5 chords" and double stops?
(note I'm referring to true "power chords: that is root and fifth only; no octave of root)

2 - Statement for context of question:
I refuse to say that [5 chords] and [5 chords plus octave] are the same kind of chord
To me that's makes about as much sense as saying an A chord and A7 are the same.
They sound different in character to me.
Absence of octave = a more raw sound
extra note = different mood = different type of chord = different name.

So I'm tentatively calling the former "enriched power chords"; as opposed to the former being simply "power-chord"
(i need names to off-set formulas in the chord-formulas chart I'm making)

So my second question is:
would it be correct to say the formulas are
root + 5th = "power chord"
root + 5th + 8th = "enriched power chord"
this question is in regards to "are the formulas correct?/ is that how one would state the inclusion of an octave of the root in the formula?" rather than
"do you agree with these names?"
The names are really just for my own understanding... eliminating any ambiguity in regards to chord formulas.

Hi Whune:

1. good question! I never thought of it before. I think that technically they are the same thing, but that double-stops are usually referred to in a lead context.

2. to me the difference between an A and an A7 is greater than the difference between the two power chords you mentioned, but that's just me. There definitely is a noticeable difference in sound with those power chords.

your formulas look correct.

1. A power chord is a specific type of interval, whereas a double stop can be any type of interval.
2. A power chord with the octave in it is still a power chord. Yes it sounds different, but that doesn't come into play when naming chords. A and A7 are different chords because they have different notes in them.
If we take A major (A, C# and E) and rearrange the order of the notes so it reads C#, A, E is it still an A major chord? Of course it is! Does it sound different to the root position chord? You bet.

Your formulas for power chords are correct though.

Power chords aren't really chords at all, they are intervals of a perfect 5th. Power chord is kind of a "guitarist" terminology.

Double stops are also two note intervals, could be 5ths, 3rds or 4ths etc. I would agree usually more of a lead context.