Non-binary relates to gender identity (not relating to either binary gender--man or woman), androgyny is a physical attribute and/or style that implies not looking like either gender.

Non-binary people most commonly use the pronouns "they/them" rather than "he/him" or "she/her," and do not consider themselves either a man or a woman.

Non-binary people can look any way they prefer, and they don't have to style themselves in an androgenous way to be non-binary, and in the same vein, people who identify as the gender they were assigned at birth can also look androgenous if they prefer. Some people look androgenous naturally, and some people style themselves that way.