Is cyclocross tire (CX) taller than normal road bike's?
BB height is a measurement that depends on too many ill defined parameters to be useful.
A rough approximation for three height of a tyre is to take its nominal width. That leaves us with a discrepancy of about 8 mm. Spezialized seem to have used either a height from the tyre manufacturers data sheet or actually measured themselves.
Tyres deviate from a perfect toroidal shape. For example, a fully inflated tyre on a narrow rim might be much taller. Rim and casing will determine the actual cross section.
There is also a layer of thick rubber to roll on and, in the case of the CX tyre knobs.
Lastly, for a real measurement one has to consider tyre drop* of the tyres. For road riding up to 15% is typical. CX tubular tyres might be depressed by 50% however.
Finally, Spezialized's road section might use different conveniens l conventions than their CC section or MTB section.
Overall there is so much guesswork in interpreting that value that you might only find out that BB height means by asking Spezialized themselves.

Tyre drop is a measure of the reduction of a tyre's extension in radial direction under a radial force oriented towards the hub.