A resume is an organized list of work experience and skills relevant to a hiring professional, while a bio is a short essay used to paint a less-formal picture of a candidate, complete with life history and non-professional information. Bios are generally are not used for hiring purposes.
A resume lists specific details about one's professional history, including, but not limited to, professional positions held, specific job duties and accomplishments, certifications, degrees, awards and relevant dates for all included accomplishments. A resume builds up an image of one's work history, and is specifically used to persuade a hiring manager or human resources person to either hire a candidate or move them along in the hiring process.
A bio, short for "biography," is a description of someone's life, including non-professional details written in prose format. Typical uses for bios are inside books to describe an author, in conference pamphlets to describe speakers, or in academic directories to describe professors. A bio is used to establish a person's professional credibility in a situation where a resume would be either too formal or too lengthy to use. In addition to prose, a bio can also include pictures, quotes from outside sources or other sources of information not generally used in a resume.