Keith Bond explains the difference between your Artist Statement and Biography very well in this article that appeared in the FineArtViews Newsletter.

The Artist's Statement vs Biography
by Keith Bond

Keith says..
Do not confuse an artist statement with a biography. Many artists often combine the two into one document that lacks the intended focus. I have probably been guilty of this. They should be two separate documents with different purposes.

Artist Statement

1. Should be brief - only a couple paragraphs.
2. Should be written in first person.
3. Should be about your current art - not past periods.
4. Should evolve and grow along with your art.
5. Should compel the viewer to want to look at your work.
6. Do not include bio info here.
7. Do not include teachers or others whose work has influenced yours. This is a statement about YOUR art, not theirs.
8. I want to repeat #5. This is the most important thing to remember - your artist statement should compel the viewer to want to look again at your work.

Biography 

Many shows and exhibits will request a bio from you. This is an important document to have.

1. Most bios are extremely boring. Mine included. Most artists bios read almost identical to each other. Again, mine included. That is why I am working on rewriting mine. I want mine to stand out and be different. I want it to be read and not tossed aside after the first few words of the first sentence.
2. In a nutshell, your bio is basically your resume written out in paragraphs. It includes the highlights from your resume, not necessarily everything. But remember, spice it up a bit (see #1).
3. Should be written in third person.
4. Include a description of your current work.
5. Here it is okay to include your past - including art instruction, influences, and what events or upbringing have shaped your artistic direction, etc.
6. Include important exhibitions or venues.
7. Include important collections or commissions, accolades, awards, etc.
8. Include where you were born and where you currently live.
9. This document should also evolve and change along with your career. More important items will be added as your career grows and less important or less relevant things will be removed.
   (Where you were born should remain the same, though ;-) ).
10. It will likely be longer than your statement, but do not make it too lengthy. Most people will not read it if it is too long (unless you have a very compelling or entertaining story).

For tips on writing an effective Artist Bio and Artist Statement for your About the Artist page, see the following articles.

Artist Bio vs. Artist Statement vs. About Page
by Alyson Stanfield, Art Biz Coach

How Your Artist Statement Can Engage More Eyeballs
by Alyson Stanfield, Art Biz Coach

3 Thought-Provoking Questions for a Better Artist Statement
by Alyson Stanfield, Art Biz Coach

Your Artist Statement Is Like A Coconut
by Alyson Stanfield, Art Biz Coach

5 Painless Fixes for a More Potent Artist Statement
by Alyson Stanfield, Art Biz Coach

Rework Your Artist Statement with 3 Answers
by Alyson Stanfield, Art Biz Coach

16 Ideas for Repurposing Your Artist Statement
by Alyson Stanfield, Art Biz Coach

Hone Your Artist Statement
by Alyson Stanfield, Art Biz Coach

Suggestion for improving your artist statement
by Alyson Stanfield, Art Biz Coach

How to Write a Good & Effective Artist Biography 
by Light Space & Time Online Art Gallery