Caliban in the Tempest is treated as a savage by Prospero and Miranda. His upbringing, more than his appearance, is what causes this, as his mother is a witch and he is considered untamed, ill-mannered, and uncultured by Prospero and Miranda. He is uneducated. He follows his impulses, which is why Miranda fears him--he follows his natural impulses towards her, and would probably have raped her if Prospero hadn't kept him in line by magical means. He is also savage in his appearance in that he does not know how to dress or look like someone with status. He is of low birth, and is nothing like a "noble savage"--he looks and acts as a savage would act, and he smells.
John the savage, on the other hand, is handsome, and is treated as something of a celebrity when he is brought back from the hinterlands. People invite him to parties and are happy to be around him. He is more like the "noble savage" for he is both a child (literally) of the so called civilized culture, he is a cultural child of the "savages" (mexicans). People treat him like a beloved outcast--they are horrified yet enthralled by him. He does not fit within their society any more than Caliban fits within Miranda and Prospero's. His upbringing has made him alien. He can be made to appear to be a part of society, but his values are so different that he can't be a part of them. In fact, when he tries, he can't live with himself.