A robber is someone who steals from another person. A bank robber might steal money from a teller by claiming to have a gun, while a robber baron is much more subtle.
Robbery is the crime that robbers commit, taking someone's property or money by hurting them or threatening to hurt them. You might picture train robbers in an old Western movie, galloping away with their loot shooting their guns in the air. In the nineteenth century, Americans began using the term "robber baron" to mean wealthy, unscrupulous businessmen.