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.