A question about chords

Alright so I've been playin guitar for 6 or so years on and off, and I'm just gettin' into theory. I barely know the basic basics, but, in theory (HA!), if:

|--2--|
|--3--| Is a D chord,
|--2--|
|--0--|
|--x--|
|--x--|

Than is:

|--14--|
|--15--| Also a D chord?
|--14--|
|--0--|
|--x--|
|--x--|

Do you kinda get what I mean? Would the chord shown in diagram 2 be a D?
And same goes with all open chords...

Thanks :)
Dave