Let's look at some useful common usage for modern city life. 1. burn up Example: I go to the gym three times a week to do cardio exercise to burn up extra fat. 2. burn out Example: After working for ten years as a foreign exchange trader, he is totally burnt out. The primary meaning of "burn out" is "cease to function as a result of exhaustion or excessive heat or friction", though if you use it with an object, it cam mean "make homeless by destroying his home by fire" or "drive very fast". The two phrasal verbs are not interchangeable. Are they similar? Not really. I think you need to cultivate the habit of using a good dictionary.

I would add that "burn out" when used like "he burned out" means he lost his enthusiasm for something because he had worked too hard at it. " He burned out at his job because he worked 12 hours each day."

The meanings are similar and overlap. "Burn up" puts the emphasis on the fuel. The fuel is completely consumed. "Burn out" puts the emphasis on the flame. The flame is gone. "I'm cold because the campfire burned out. Those pine logs burned up too quickly."

They have similar meanings. Burn up usually refers to items that are consumed by fire; wood, paper,etc. Burn out can have a couple meanings. For example, you can do a burn out with your car; when you spin your wheels on dry asphalt creating a big cloud of smoke. Burn out is also a method to clean an oven or furnace. Hope this clarifies the two expressions.

I agree with Joel that "Burn up usually refers to items that are consumed by fire; wood, paper,etc. " That is the literal definition. There are also metaphorical uses such as "he is burning up with a fever". Of course, he is not literally on fire but his body temperature is hotter than normal. Ben is also right that "burn up" and "burn out" are not interchangeable. As he wrote, "The primary meaning of "burn out" is "cease to function as a result of exhaustion or excessive heat or friction". The best way to understand "burn out" is to think of a motor that "burns out" because of excessive speed or lack of lubrication. Also, a light bulb can "burn out". The filament burns instead of glowing and the bulb ceases to function. Hope that helps.