Native English speaker here. To tease is more or less to make fun of someone but to taunt them, you're inciting them to act upon what you're saying or doing. For example, I can tease you about your shirt but if I'm taunting you, I'm almost challenging you to react.

Teasing: A. Is intended to get both parties to laugh. B. Isn’t intended to hurt the other person. C. Pokes fun in a light-hearted, clever, and benign way. D. Allows the teaser and the person tease to swap roles with ease. E. Is discontinued when person teased becomes upset or objects to the teasing. Taunting: A. Includes laughter directed at the target, not with the target. B. Is intended to harm. C. Involves humiliating, cruel, demeaning, or bigoted comments thinly disguised as jokes. D. Is based on an imbalance of power and is one-sided: the bully taunts, the bullied kid is taunted. E. Continues especially when targeted kid becomes distressed or objects to the taunt.

Hi! My interpretation of it (I'm a native speaker but can't claim to know for sure) is that taunt is harsher, meaner and more extreme than tease. It is definitely malicious, intended to be critical. To my mind, it also suggests it occurs more than once, but that might not be accurate. Tease can be malicious but is lighter, and can also be seen as playful, or done in an affectionate way, sometimes even flirtatiously.