According to Bugs Bunny, hosenphefer is rabbit, but you can fool kings into just eating carrots.
California has (yet another - see Smash's previous discussion on our "here or to go" tax law) great law on this issue. I'm sure some long time residents will recall voting on it. I think it was around 1992 or so. We made it illegal to use horses raised in California for pet food in California. I'm not sure the details - if the food can't be sold within California or if it can't be made in California. Anyhow, we have the initiative system which allows virtually any interested party to hire people to get a law on the ballet. This gem was actually put on by out of state ranchers who apparently make a killing off of it.
Back on point, the cow is still a cow. The meat is renamed when it is put to use, but so is the hide, for example, which is now leather. Other parts are used, too. IIRC some are renamed such as the spinal column/brain tissues which are supposed to be segregated so we don't eat them. To just refer to the whole thing as cow now is less information then needed, and specifying each piece by location or muscle group can become longwinded.
But I think what you are looking for is the dissociation between animal (cute, furry, gentle and/or lovable) and the meat which so many people choose to consume.
As to the joke about horse==whopper, actually after the e.coli scare (one of the many, but the one where the young people died in the Pacific Northwest - one of the more severe) fast food joints (national chains) buy a pretty good brand of beef. Grade A beef just isn't very expensive compared to, say, labor costs or the cost of the building in the industry. The truely poor beef which is still judged fit for consumption by humans (I think it is grade D) is mostly sold to prisons and the school lunch programs - I'm citing Fast Food Nation by E. Slosser here (and there are references in it which you can follow if you are interested from there).
Back off topic: there is a great joke song titled something like "Cat in the Kettle at the Peking Moon" to the tune of "Cat in the Cradle" by Cat Stevens (or Harry Chapin? ...alas early alzheimers).