Hehe, sorry. There's no reason red lasers would inherently have larger beams. Not single-mode ones at least. Its just that in the portable reds, everyone seems to use an Aixiz module or a lens with a similar focal length. Therefore the reds have a thicker beam, but better divergence than your typical greenie. All you'd need to do was collimate it with a shorter focal length lens though and you could end up with the opposite - a beam thinner than a typical greenie but worse divergence.
Always keep in mind that divergence and beam diameter are a trade off. You can always make the beam smaller, or the divergence better, but you'll make the other one worse in the process. The only thing you can't get better is the M^2 beam quality - this takes into account BOTH divergence and min beam diameter at the same time. Both single-mode diodes and greenies have M^2s close enough to the perfect 1.0. The beam specs are then just determined by how strong of a lens is used to collimate the beam (shorter focus lens = thinner beam, worse divergence).
Multi-mode diodes (IE, 660nm above 200-300mW or so, and most class IIIB 635nm) are a bit of an exception though. Their M^2 is often ~20. So you can still get beams thinner than a greenie, but you end up with horrible >10mRad divergence in the process. Therefore multi-mode reds are normally adjusted with diameters in the 3-6mm range. There's no rule saying they physically have to though.
This is why if I ever make a high power RGB, its gunna use 671nm DPSS =D. Expensive, but a nice thin red beam with decent divergence to match.