To answer your question specifically, since you are asking about words that mean a person who is poor and a person who is rich:

Poor person: pauper, mendicant, guttersnipe.

Rich person: baron, magnate, tycoon, moneybags.

In these examples, the words for a rich person are less formal than the ones for a poor person. For a rich person, you can use person of means, person of substance (both formal), fat cat, or deep pocket if you're willing to use more than one word.

To answer your question specifically, here are some words that mean a person who is poor and some that mean a person who is rich:

Poor person: pauper, mendicant, guttersnipe
Rich person: baron, magnate, tycoon, moneybags

In these examples, the words for a rich person are less formal than the ones for a poor person. For a rich person, you can use these, if you're willing to use more than one word:

person of means, person of substance (both formal), fat cat, deep pocket

On the other hand, in your comments you ask for adjectives that can be applied to a person. Some of these are:

Poor: impecunious, strapped, needy, unprosperous
Rich: wealthy, affluent, well-heeled/well-off/well-to-to, moneyed, prosperous