These are the freaks that have been modified, artefacts of demons or mermaids and circus artists who use some trick to persuade the audience that they are freak.

Devil Baby

Aka freak baby, pickled punk
A gaffed freak, usually constructed to appear mummified or otherwise preserved, often displayed in a bocal or a tiny coffin. The name is pretty much self explanatory, and they often had horns, fangs, hoofed feet, claws, ...

Pictures

Anatomical wonder

A sideshow performer, usually perceived by the public as a human oddity, but more a working act. The performer would do stunts such as 'the man without a stomach' (pulling the gut in until the backbone shows), pulling themselves through a coat hanger or tennis racket, and other Indian Rubber Man stunts.

Headless

Illusion show where a 'headless' person is displayed. They're usually pitched as 'medical miracles' following tragic accidents.

Human pincusionSpider

An act in which the performer sticks sharp objects such as pins, needles,meat-skewers,etc, into their flesh [Also known as "Fakirs"...from the Indian term...or "Pain-proof men"

Spidora or spider-woman

Illusion show in which the head of a woman appears to grow from the body of a huge spider. The illusion is a reversal of the headless illusion.