They are quite different. Let me start with "salary." A salary is a regular sum of money paid for doing work. An "allowance" is a regular sum of money that is just paid automatically and unconditionally, NOT in exchange for work. In the United States the word is used most frequently in connection with children. "My father gave me an allowance of $5 a week; I didn't have to do chores to earn it." Or, "My grandfather gave my grandmother a housekeeping allowance of $X a week." bonus is always something extra, in addition to whatever was expected. "My salary is $X a year, but we get a Christmas bonus almost every year."

An allowance is usually given for a specific purpose. For instance, some parents will pay their children a living allowance while in college. Money for food, clothes, gas, etc.. Many companies will pay their employees an extra allowance (called a per diem) for travelling, for the same reason. Food, lodging, gas. A bonus is usually an incentive or extra payment for doing very well at something, or for a special occasion. Some companies will pay extra money (红包) at Christmas time, or if an employee does very well at their job. (like getting extra sales, or winning a big account)