Are two different tires marked with the same dimensions (700 x 25c) the same size?
I'd check if the wheel was in properly and is in good condition (true) along with the tire being mounted properly on the rim.

There is some variation in tires true sizes despite being marked the same size, though half a cm would be a lot larger variation than one could reasonably expect, especially with older tires. Features like studs, knobs can also affect this. If you have reasonable clearance for a given size of tire, one should reasonably expect a similar tire from another manufacturer to also give reasonable clearance, though this is not always the case.