Many of those that sport shoot coyotes or rabbits or whatever may claim that it's for some noble cause... some are legit. I think you would be naive to believe that there aren't some folks who just enjoy it for the sheer rush, or maybe it's just boredom or low self esteem... psychology is a funny thing.
I have acknowledged that by my mere existence creatures die. They die for my food; they die for my housing; they die for my transportation; and they die so that I may shop, watch movies, use bleach as a cleaning product, etc. Here's the difference: I try to avoid "consumerism" as much as possible and I don't enjoy the fact that I'm taking creatures lives.
That said, I've NEVER intentionally killed anything breathing creature for the enjoyment of it or just because I could. If I ever have killed a living breathing creature it was incidental, accidental, or truly necessary (as opposed to whimsical).
Finally, humans don't get a pass by animalistic behavior in society. The fact that animals kill for sport is immaterial. We're logical thinking beings who understand the ecosystem. Further, a single coyote can't kill 14,000 rabbits in a night.... the few it kills don't affect the ecosystem. Contrast that with some yahoos with rifles out blastin' away at as many coyotes or rabbits or whatever that are arbitrarily on the horizon. And, the coyote may be practicing his TRUE hunting skills for which his survival depends when he stalks and kills for sport. He is using his muscles, keen senses, balance, dexterity, silent stalking skills, and ultimately his fighting and killing skills, taking down his prey and killing it efficiently. Contrast that with the yahoos in the back up pickup trucks shinning rabbits, deer, coyotes, you name it... or how about the skillful and couragous sportsman who slugs beers whilst sitting in a deer blind all day, only to see and spot the prize coyotes in the field. He boldly raises his $1500 +/- rifle with 3x9 scope, raises it and rests it on a limb for balance, clicks off the safety, gathers his target in his illumiated crosshairs, takes a breath, and with all his might and coordination sqeezes that 2 pound trigger. Wow, I'm impressed at how that man has really improved his profound sport hunting skills. Then he goes home, swinging by McDonalds for a super size meal on the way, to catch the highlights of the baseball game on ESPN whilst enjoying a cold brew....
Difference? If you can't see the differences I can't demonstrate them any more clearly.