I suffer from depression, which I know is a mental illnes, but isn't Aspergers a form of Autism, which isn't a mental illness, but a disorder?

Major Depressive Disorder is a mental disorder. Asperger's Syndrome is also mental disorder. People often call it 'mild' Autism, so, yes, it is a form of Autism, but true Autism is more severe. You could call Asperger's a "mental illness," but most clinical experts would probably avoid the word "illness" because it is quite harsh. If you have Major Depressive Disorder you can call yourself "mentally ill" too. The question is this: Would you like people to refer to you as mentally ill or as having a mental disorder? It's a pretty personal choice.