Mace is just a brand of pepper spray, so they really do not have any major difference. Aside from Mace, there are more pepper brands spray that people can choose from, depending on their availability in the market. Pepper spray and Mace contain oleoresin capsicum, a chemical that is also found chili peppers that can cause irritation to the eyes and skin.
Mace is known to have been producing pepper sprays in different colors that look like a revolver. A normal pepper spray has a shorter range (about 2 feet max) while Mace can spray up to 20 ft. There are a handful of guides and instructions on the Internet on how to DIY a pepper spray. Mace, on the other hand, is readily made that people can easily use.
For protection, people will often arm themselves with pepper spray. They will use this device to disarm or harm the attacker. Usually, you spray the pepper spray in the face hoping for the shower to make contact with the eyes. Their eyes will burn, and they will be in pain. Pepper spray was made to cause people pain and stop attacking.
However, two words are used to mean the same thing. One is mace, and the other is pepper spray. However, there is a big difference. Mace is the company or brand name that makes one kind of pepper spray. Different types of companies produce pepper spray. However, over time, people use both words to mean the same device.