Cardio is really a modern term that has grown to replace aerobic exercise. To avoid the stigma of the aerobic craze of the 70s people switched to cardio when discussing it relative to fitness and strength-training programs to disassociate with the aerobics-only phenomenon.
Cardio is short for cardiovascular exercise which means really any exercise that benefits the heart. This used to be mainly aerobic training but now research suggests that weight lifting also benefits the heart - this is an example of a phrase that became popular before science could really validate it.
Aerobic exercise is any sustainable activity that utilizes oxygen (ergo the burning of fat) for a primary source of fuel. Weight lifting that is intense and in short duration will primarily use stored glycogen and the ATP-CP pathway (intramuscular energetics with creatine phosphate that - adenosine triphosphate or ATP is broken to adenosine diphosphate and this releases energy. To rebuild ADP to ATP, the CP is split, lending the extra phosphate moelcule needed for ADP to become ATP and thereby fuel another reaction).
Now, this definition is muddied because you can have weight training i.e. longer sets that actually use oxygen and are therefore more aerobic (take circuit training, for example, when people aren't using a heavy load). You can also have what is traditionally thought of as cardio i.e. sprints that can be anaerobic depending on the rest. If the heart rate is allowed to lower between the intervals followed by maximum output then you are more in the anaerobic/glycolytic range. If you are only doing intervals but the heart does not drop substantially then you are going to be in more of a cardio range.
Basically, and this is a nutshell, oversimplifying because I've already gotten quite technical, there are primarily three systems that fuel energy. ALL energy systems are used to some extent, but various activity will use more of one or the other.
Anything lasting just a few seconds is going to be primarily anaerobic and use the ATP-CP system. This includes weight lifting, where the reps last a few seconds and are maximal bouts of output. Active rest occurs between the repetitions and then actual rest occurs between the sets. Shot-put, 50 yard-dash, weight lifting, olympic lifting, power-lifting are all examples of this.
Anything lasting a few minutes is primarily the glycolytic system where lactic acid is utilized to generate energy. This would be prolonged bouts such as sprints, longer weight lifting sets, etc. Basketball (run down court, then stay at the court = submaximal bout followed by active rest), and Soccer are examples of this.
Anything beyond that first few minutes must utilize oxygen turnover and therefore you are in the aerobic zone. This would be longer runs, rowing, hiking, etc.
Now, keep in mind there is no black and white with this - you still cross over into multiple systems. The reason why HIIT is more cardio than, say, a 20 minute weight training session, is that in HIIT on the slower intervals you are still performing work. Your heart rate drops somewhat but doesn't drop a lot and therefore is still elevated in its output - this means that oxygen must fuel the process. On the other hand, in typical weight training, you are resting between sets which allows adequate recovery for the heart rate to slow while the muscle energetics replenish themselves.
A long weight training session with short rest and a lot of supersets is going to be aerobic at the same time as being anaerobic during the sets - you are anaerobic to explosively move the weight but because you are not allowing your heart rate to drop significantly between bouts of work the entire workout becomes more aerboic. Dave Draper was a huge advocate of this method of training and felt you could build muscle and stay lean or even burn fat simultaneously by supersetting a lot. Looking at his physique I don't doubt there is some validity there.
Hope that helps - if you really want to dig into the details just search on ATP-CP or muscular energetics and you can get some good primers. Of course, then you might be forced to look into the Krebs Cycle and other pathways of metabolism and discover just why it is a gross oversimplification for people to say "this exercise burns muscle" or "if you exercise on an empty stomach your body is forced to burn fat"
