TO RESIGN is to quit a job. TO RETIRE is to stop working when you are old. They both mean TO STOP WORKING, but TO RETIRE can also mean to stop working with a specific company after many years. Typically when one retires, he or she is paid a small amount by the company every month based on how long he or she worked for the company.

retire is when you leave your job because of old age, whereas resign means to give up a job (no age factor, it's just a personal decision to quit)

You retire once you get older or have been with a company for a very long time. Once you retire from a company you continue to get money. When you resign you are quitting and you don't receive any more money from them.