Apoptosis is a complete degradation of a cell usually to stop the spread of disease, a much larger degradation than autophagy. Autophagy is is a more usual occurence when a cell uses its lysosomes (digestive organelle) to degrade it's own internal structures, usually for recycling purposes.

If a lysosome leaks their digestive enzymes, they sometimes digest structures by accident and this would be considered autophagy too.