The original release of the the
Nintendo Entertainment System in 1985 included a dark gray Zapper with light gray highlights and a bright red trigger. Apparently some people believed that these colors made the Zapper look too much like a real
gun (you know, because so many people owned
laser pistols in the late 1980s) and the next generation of Zappers (i.e. the next manufacturing run) introduced a color change in the gun. The new Zapper was bright orange in color to show that it was
obviously a toy. This model also had a black trigger, but the light gray highlights remainded. There is no technological difference between the two guns; they both operate the same (and they both make that neat "KA-PWANG" sound when you pull the trigger).
Incidentially, it's often quite easy to find a used Zapper for sale at used game stores or online auctions for under $5. What can be difficult is finding a used gray Zapper for sale at a reasonable price. Seeing as how the gray models are older, they've been around for longer and have taken more abuse, so there are statistically less of them in circulation. Furthermore, many younger gamers felt jaded by the Zapper (gray or orange) since it was playable with so few games and cut off the cords so they could play with the Zapper itself as if it were a real gun, thereby further lowering the amount of active Zappers in the wild. Some people feel that since the gray model was discontinued it's more valuable than the orange model. This argument is hollow seeing as how both models are no longer produced, so both models are worth the same in that regard. Orange zappers are more common in the used game market, but the gray ones are out there. Don't let anyone talk you into paying big bucks for a gray Zapper.
And don't even try to shoot the dog. You just can't. Accept it.
References:
http://db.gamefaqs.com/console/nes/file/nes_zapper.txt
http://www.eBay.com