So you need to be clear what concept of fairness or equity or justice is being used. There may be markets in goods and services, and there may be markets in factors of production like land, labor, and capital. Financial assets may also be traded on markets. But the market in general has no clear meaning, and should not be used as a synonym for a national economy. If you are engaged in a theoretical discussion of different ways of allocating goods, as in markets versus central planning, it might be reasonable to talk about properties of the market in the abstract.
Money is a name given to certain kinds of assets.
Money is not income. Money is not spending. Money is not wealth. If you mean income or spending or wealth, use those words. All are vague terms that must normally be defined or specified further.