Conti's standard glue is optimized for aluminum; the carbon-specific glue is optimized for carbon. They aren't willing to divulge to us the science behind what makes the carbon-specific cement carbon-specific, no doubt fearing the rise of a Competitive Cyclist tub glue competitor. All the same, Continental assures us that either will work on either rim, just the specific glues work better with their intended rims.
Regardless of Conti's assurances, we recommend going with the standard option for alloy and the carbon option for carbon. To justify our position, we refer you again to the above Beloki reference. That crash may have been caused by melting glue on a hot descent with heavy braking, but there's no reason to add any more risk than necessary.
Despite the presence of whatever alchemical agent recommends the carbon cement for carbon rims, the two glues are about the same in terms of texture, viscosity, curing time, etc. A single 25g tube of Continental Carbon Rim glue should be enough to secure one tire to one wheel, with maybe a little left over.
Secure your tubs in rim-appropriate confidence
Standard cement allies with alloy rims
Carbon rim cement secures tires to carbon