From Merriam-Webster:

Theft: an unlawful taking of property

Robbery: taking of property from a person by violence or threat

Burglary: the entering of a property with the intent to commit a crime

See the difference? A robber takes your wallet from you; a burglar breaks into your home; and they are both thieves if they successfully take something.

A thief usually steals secretly and the victim usually becomes aware of the theft only after something has been stolen.
A robber is not only usually seen by the victim, but also often injures or threatens to injure the victim (or use some other type of force) during the robbery.

A thief will usually strike at any time of the day, whereas a burglar prefers to work in the dead of night, whilst his victims are sound asleep.