The key issue that all campers have in common is perishability. Even RV campers, who have access to a small refrigerator, often need to consider choosing foods that do not actually require refrigeration to prevent spoilage due to space and possibly electricity supply issues. Tailgate campers can use coolers, but these are also of limited capacity and capability (or will be unless regular trips are made to get more ice). Finally, there are backcountry campers, who have no access to refrigeration of any kind. Thus, to varying degrees, all campers need to choose foodstuffs that won't easily go rotten.
The RV campers have the most options, and their food choices are only slightly different than cooking at home. They almost always have a small refrigerator, and the main limit on that is space and getting an electrical hook-up. Furthermore, an RV camper does not have a serious problem with storage space and weight for things like dry goods, canned goods, and things like root vegetables (potatoes, onions, carrots), bread, rice and pasta that have a decent shelf life. The only thing that really separates the pantry of an RV from the pantry at home is how far away the supermarket is, and therefore how much trouble it will be to re-stock or to get particular items. Otherwise, literally anything goes when it comes to foodstuffs for RV camping.
Tailgate campers occupy a happy middle ground between RVs and backcountry campers. As their campsite is rarely far from their car or truck, these campers don't have to worry about weight. However, their ability to preserve perishable food is limited to coolers for the most part, which means those should emphasize fresh meat, dairy, cheese, eggs, and other things that absolutely need to be kept cold. Otherwise, the fact that they can keep a store of heavy foodstuffs in their vehicle means they can make choices a backcountry camper cannot: long-lived fruits like apples and pears, root vegetables, bread and heavy tin cans. The main thing for a tailgate camper is to be very choosy about what highly perishable items to bring along, if they bring any at all. Otherwise, they can bring and cook just about anything they want.
The backpacking, backcountry camper has to carry in everything they eat, unless it is caught or foraged. That means they have the most demanding grocery list of all campers. In addition to perishability, backpackers need to weigh the calorie-to-weight ratio of their foods, to get as much energy per ounce as they can. The best food of all for this is trail mix. Nuts have more calories per ounce than even table sugar, and dried fruits are a good source of vitamins. Other options include pasta, ramen noodles, granola, corn chips, dried vegetables, rice and beans, beef jerky and dried food packs.
Caught and Foraged
Other foods to cook while camping are things you can get from the wild. Many people go camping to be close to good fishing, and a good catch of fish makes for some yummy eating by the campfire. Hunters do much the same. Going for a hike is a good time to practice and develop any skills in foraging for wild, edible plants, and these can be immediately put to use on the camp dinner table.