Quote:
Originally Posted by jwight
Correct me if I'm wrong here, but wheels don't have profiles, high or low. A 15 in wheel is a 15 in wheel. Tires do have profiles, as indicated by their designations; a 70 series tire is high profile - more distance between the inside and outside diameters. A 35 series tire is low profile - less distance, therefore less "give" to protect the wheel rim from potholes, etc. 
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A 15" wheel is indeed a 15" wheel. (There are different offsets and widths to contend with, but that has nothing to do with tire size.
The "series" of the tire is a measure of sidewall to tread ratio (aspect ratio).
A 15" wheel with a 175/55/15 has a 3.8" sidewall. A 15" wheel with a 195/55/15 has a 4.2" sidewall, but of course the diameter is now larger as well.
A 205/45/15 has just about the same sidewall at 3.6" as the original 175/55/15, but has a 45 vs 55 aspect ratio.
This page,
Tire size calculator , contains a pretty useful tool for understanding what different tire/wheel sizes will change.
And yes, all things being equal, a taller sidewall will protect a given wheel better than a shorter one. As in the Mazda 3 example, the stock tires on the wagon are 205/50/17, with a 4" sidewall. The 205/55/16's are the same diameter, with almost a 1/2" more sidewall.