What is the difference between a hermaphrodite and a tranny?

A hermaphrodite is an individual that was born with both male and female genitalia. Doctors will usually remove what to their best estimate is the non-functional genitals, and tell the parents to raise the child as the gender best represented by the functional one.

By 'tranny', you can mean either 'transvestite', 'transgender', or 'transsexual'.

A transvestite is someone who enjoys dressing in clothing traditionally worn by the opposite sex (usually refers to men who wear women's clothing, since in the West, women often wear trousers).

A transgendered individual is someone who is living as an individual of the opposite physical sex, usually (but not always) prior to having a sex change, which would then make said person transsexual.