AMG is now owned by Mercedes. Till 1990 AMG was a separate firm. well basically almost every class of Mercedes except couple have a trim level which is classified as AMG. All AMG have bigger engines plus.. more sophisticated mechanical and electrical equipment as well as a distinct body and styling. there is a huge price difference. its like "S" in Audi or "M" in BMW. just go on the links below and you will see the comparison.
In simple world its like Shelby/ Ford/ Mustang :D
C class Compare Mercedes C-Class Luxury & Sport Sedans | Mercedes-Benz
<a href='http://www.mbusa.com/mercedes/legacy/vehicles/models/class-C/bodystyle-CPE'>Compare Mercedes C-Class Luxury & Sport Coupes | Mercedes-Benz</a>
M Compare M-Class SUVs: ML350, ML550, ML63 AMG | Mercedes-Benz
S Compare Mercedes S-Class Luxury Sedans | Mercedes-Benz
CL Compare Mercedes CL-Class Luxury Coupes | Mercedes-Benz
GL Compare Mercedes GL-Class Luxury SUVs | Mercedes-Benz
G Compare Mercedes G-Class Luxury SUVs | Mercedes-Benz
SLK Compare SLK-Class Roadsters: SLK250, SLK350, SLK55 AMG | Mercedes-Benz
SL Compare Mercedes SL-Class Roadsters | Mercedes-Benz
SLS Compare Mercedes SLS-Class AMG GT Coupe and Roadster | Mercedes-Benz