Let's clear this up once and for all, since both Gary and I posted information that isn't totally correct. Though it sounds like the OP has moved on, perhaps this will be useful to someone doing a search...
As Gary points out, "Pipe" (which is round) is specified by a nominal size (ie 2") and a "Schedule" of 10, 40, 80, or 160 that determines wall thickness. The OD is fixed, at a size larger than nominal, with ID of Schedule 40 pipe being roughly the nominal. For example, 2" Pipe has an OD of 2.375" regardless of what Schedule it is, and the ID of 2" Sch 40 pipe is very close to 2". (I believe I suggested that the ID was always 2" above, and that's not correct.)
Round "Mechanical Tubing" (ex DOM, CDS, ERW) is specified by a true OD and either wall thickness or ID, depending on type. (DOM is OD/ID, other tubing varieties are OD/wall thickness.) These dimensions are tightly controlled by ASTM A513 for DOM, and A519 for other types. Thus 2" OD round "Tubing" is always exactly 2" OD.
Square and Rectangle "Mechanical Tubing", is generally governed by ASTM A513 or A500, depending on size. As with round "tubing", the measurements given are exact outside dimensions. IE, 2"x2" square tubing is exactly 2" outside regardless of whether it's 16ga or 1/4" wall.
I believe Gary may have been thinking about Conduit rather than Mechanical Tubing when he made the comment above that tubing is sized by ID for round and square... I believe that is true for round conduit, but I'm not sure I've ever seen square conduit, and I've not seen any choice in the wall thickness of conduit either... I guess I'm not sure what he was thinking of, but the above is true, and can be verified.
Thus concludes today's lesson for us all.