Are Amoxil and Cefalexin the same?

Not exactly. Augmentin contains Amoxicillin and another drug, clavulonic acid. The latter augments the antimicrobial spectrum of Amoxicillin. Amoxicillin is a penicillin-like drug effective against certain types of bacteria, unless those baceria possess the enzyme that can inactivate these types of antibiotics. This enzyme is called beta-lactamase. Some bacteria have the ability to make beta-lactamase and some do not; some bacteria can develop the ability to make beta-lactamase if exposed to penecillin-like drugs over a period of time (one way bacterial develop resistance to antibiotics). Clavulonic acid blocks beta-lactamase, allowing the amoxicillin to work on bacteria whether or not they possess beta-lactamase.