Wage and income are not totally referring to the same thing, but they are interrelated. Wage simply means the amount of money paid to someone for a specified quantity of work. Wages can come in different ways. There are some you get on a monthly basis; there are some you get on a weekly basis, you get some on a daily basis, at times you can have your wage on an hourly basis.
How you want to be paid depends on the nature of work and the agreement reached between you and your employer. Income, on the other hand, means the amount of money you get by working or by capitalizing on the work of others. You get income on any business you enter into and not a wage. Income is the totality of all the money you have from all other sources. Wages are also part of your income. Another difference is that you can get income without necessarily working for it, while you will need to work before you can get your wage
Hicks and Slutsky may be confusing to people who have never tried to know more about microeconomics. If by any chance that you need to know more about this now, you should know that HIcks is the method that will be used when the consumer would need to be compensated for the amount that has already been used.
Slutsky is another method that will allow the rates that need to be paid for by the consumer to be greatly lessened. This means that the rates that the consumer needs would become affordable. These are methods usually considered by companies who would like to be noticed more by consumers. They also want to make sure that they will provide what their customers want.