700c/29" is six of one/half-dozen of the other.

It's driven by an industry who can't decide how they want to market things, so generally speaking, inches refer to mountain bikes, French sizing to everything else. Mechanics use ETRTO sizes, as it leaves no room for miscommunication. 622, for those sizes, for what it's worth.

There may be differences between a 100mm wide, 15mm diameter axle for a road vs mountain bike, but the only significant one, aside from fashion (see: low spoke counts, weird spoking patterns), is a wider rim on the mountain bike vs the road bike.