I noticed while changing different wheelsets on my bicycles, that some of them are larger than the others.

Case one:
Tires are Schwalbe Lugano 700x23
Unknown 700c rims laced to Shimano 600 hubs. Low profile, probably typical mid 80s clincher rims.

Switching the same tires to Mavic CXP33 rims laced to Shimano 600 6500hubs, I noticed that my rear wheel cannot fit into the rear triangle while the tire is fully inflated, so I have to insert the wheel and then inflate the tire to proper pressure. Also, I had to lower the brake pads, farther from the edge of the tire, since the brake pads won't fit the same position and would rub the tire.

Case two:
Tires are Vittoria Rubino 700x25

The same Mavic CXP33, but I had the front wheel re laced with Remerx Taurus, and now I notice that the top tube on my non sloped steel bicycle is not parallel with the ground anymore. Also, I had to move the brakepads all the way within the short reach of the brake calipers.

So, while using same tires, I noticed the complete wheel size actually does change depending on the rim.

http://sheldonbrown.com/rim-sizing.html
Bead seat diameter is standardized 622mm, right?
So the tire should fit on all rims the same, though inner width of the rim surely dictates the height of the tire in the end! Too bad I did not have info about the inner rim width of the unknown rims from the start of the story, but it does make sense that with smaller inner rim width, the clincher is deforming verticaly. Is this really the case? Mavic's have ETRTO 622x15 and Remerx's have 622x14. Does that 1mm tighter space really increases the vertical size of the tire?

I will relace the rear wheel to the same type of Remerx rim, and if the bicycle does not level the top tube, I'll suspect at the bent fork

Anybody care to share some practical knowledge regarding this topic? I'm having difficulties searching anything related to it.

Thanks