I know what camping is, but what are frontcountry and backcountry camping?
Front country is a rarely used term; it would only be in contrast to backcountry. Backcountry camping means that you are not near the road or in a developed area. Typically sites can only be reached by foot or boat, often several hours of travel from any development. Facilities will range from absolutely nothing - camp where you like, try not to make a mess - to spartan - a sign on a tree, a ring of stones for a fire, a latrine pit with a wooden box on it. Your behaviour will typically be more restricted (eg no cans or bottles may be brought) than in a developed campground.
Front country camping is what I call car camping. There are sites with picnic tables, fireplaces, possibly grills, taps, central bathrooms with sinks, perhaps even flush toilets or showers, electricity, there might be a store or an office with a phone, and it's on a road so you can go out and get things if you need them.
Neither one of them matches festival camping, which is a farmers field full of tents with no real camping support (fireplaces, picnic tables) but plenty of event support (food stalls, entertainment.)
You can ask questions about the details of any kind of camping here on The Great Outdoors, btw.
Where I live (Outside US), Front-country is used to refer to facilities and activities that are close to roads and easily accessible. Short walks, nature trails etc 10 minutes up to a couple of hours, camps and visitor centres you can drive to are "Front Country". Front country is often wheel chair accessible, suitable for all fitness and age levels, although extends to some longer hikes in more remote areas that are heavily used and require high levels of signage and maintenance. Facilities are well maintained and cleaned regularly. Users are typically townies and tourists in street cloths and street shoes and young families.
Back-country are remote locations - typically more than 4 hours walk from a formed road, although 4x4 trails and farm access tracks might get you into back country, if you can get there in a 2wd car, its probably not back-country. Facilitates are basic. Huts and Shelters have limited facilitates - often no cookers and sometime not even heating (despite sub zero temperatures) -think one step up from a tent. Tracks are rough or just marked routes, bridges across rivers are basic swing bridges, 2/3 wire bridges. Unlike front-country users, back-country travellers are expected to be competent and self sufficient. Safety and comfort are the users responsibility.
"Wilderness Area" is defined at least eight hours walk from nearest road end.
I have mostly commonly heard those two terms used together in skiing. Frontcountry is lift served skiing inside the resort boundaries verses backcountry skiing where you ski up the hill first before you ski down it.
(i.e. the front of the mountain is where the lifts and trails are, the back is where they aren't. )
Frontcountry is a relatively new term compared to backcountry.
Backcountry in general implies a more remote setting and one that you reach only by self-propelled means. I would expect nothing in the way of facilities at a backcountry camping site.
I have never heard the term frontcountry applied to camping. But I guess it makes sense as an antonym to backcountry. Backcountry camping would generally imply that you carry in everything you need on foot and there isn't anything setup for you when you get there.
So in general frontcountry would imply some kind of facility or access that somehow make it "not backcountry".
I have generally used this term when thinking about definitive care. If you or someone you are with gets injured can you get them to an ambulance within 1 hour? YES - You are in the front country NO - You are in the backcountry (and should be prepared to be independent if any situation should arise)
Any other definition can get you into a grey area and are really not helpful in describing exactly what is happening. I've been to places that can actually change depending on the season (ie: the top of Mt. Washington, NH) The summit of Mt Washington is actually the front country in the warmer months because there is a road up there. When the road is closed...you're in the backcountry. You can find beautiful campsites with a lot of facilities but if you can't get to an ambulance within an hour...you're in the backcountry.
Also something to think about...if you are hiking for less then an hour, you still might be in the backcountry because if you or your friend gets injured it will take WAY MORE then an hour to carry them out. If you're hiking on a trail I would venture a guess that anything more then 15 minutes in could be considered backcountry.
Hope this helps!