Yes, acid reflux is simply another name for the very common condition of heartburn.
You could say heartburn describes the feeling, where as acid reflux effectively describes the cause.
The problem arises when acid in your stomach is temporarily allowed to flow back up the oesophagus (the tube that carries food from the mouth to the stomach) causing a burning feeling in the chest area, hence the name heartburn. Once this excess acid reaches the mouth, it leaves the body in the form of gas which is the reason why heartburn causes burping.
Acid reflux or heartburn, whichever you want to call it, can be effectively treated with over the counter drugs such as Zantac which block or neutralize the offending acid. Your GP can also prescribe medication to prevent too much acid production in the stomach.
However, this simply treats the symptoms of the condition and not the cause. In the majority of cases lifestyle choices are the reasons behind heartburn - the food you eat, the alcohol you drink and the stress you put yourself under. By eating less acidic foods, cutting back on the booze and trying to stay just a little calmer, you'll avoid developing heartburn in the first place.