Statement should read: "Glycolysis occurs both in the absence and presence of oxygen".
Why? Because glycolysis is just the process that converts glucose to energy in a cell.
The main difference between aerobic and anaerobic glycolysis is the presence or absence of oxygen. The other difference is in the by-products of the process.
Aerobic glycolysis has CO2 and H2O as the by-products, while anaerobic glycolysis differs based on the organism: ethanol in plants and many bacteria, lactic acid in animals and other bacteria. Humans do both aerobic and anaerobic glycolysis during exercise. Aerobic glycolysis makes pyruvate while anaerobic glycolysis makes lactate (lactic acid) - which is why your muscles hurt!
Another huge difference is that aerobic glycolysis makes a lot more ATP (energy) than anaerobic glycolysis does.
