Yes, it is possible that the tires are sized differently. Tire manufacturers have become much more consistent in their sizing, but there are still small variations.
Part of the issue lies in the fact that tire profile changes slightly depending on the rim it is affixed to. Essentially, a narrower rim will result in a larger outer diameter and a narrower profile while a wider rim will result in the tire having a smaller diameter and wider profile. But since there is no standard rim size in the bike industry, upon which rim size do you base your measurements? Different tire manufacturers have settled on what they believe to be the 'best' or 'most true', but with no consensus, there's bound to be some inconsistency.
But that's not all. There's also a historical precedent (admittedly much diminished in the past couple of decades) of tire manufacturers intentionally LYING about their tire sizing. Why would this occur? Because having the lightest tire is a sales point. But what if your tire isn't actually the lightest one out there? Well, maybe your 23 is lighter than the lightest 25, and no one's going to pull out the calipers to actually CHECK. So, just change the number on the sidewall and happily claim to be the lightest "x25" tire in the world.
Interesting historical oddity: Why do we call tires that fit on 622mm rims "700c" (actual outer diameter ~660mm) and tires that fit on 571mm rims "650c" (actual outer diameter ~610mm)? Answers: http://www.sheldonbrown.com/tire-sizing.html#french