No "roughly" about it. The "bead seat diameter" is the crucial measurement, and it is identical.

In Europe, it is common to see touring tires marked as 28" tires. That is because a reasonably wide touring tire mounted onto a 700c rim will more or less measure out at around 28".

Mountain bike tires are wider, tend to be taller, and possibly for marketing reasons as well the term 29er caught on.

The one thing to keep an eye on is rim width. Touring tires and mountain bike tires are wider than roadie tires. I have some 28mm-wide mountain-bike rims. It would be sort of silly of me to mount a 22mm-wide road-bike tire on those rims, even though the bead seat diameter would allow me to do so. Likewise, I have a 17mm rim around here somewhere. I could cram a 29er mountain-bike tire on it, but I'd probably pinch flat a lot.

So bead seat diameter is the crucial thing, but you also generally want your tire to be reasonably wider than your rim.