A thread which was opened today and then locked by a moderator provided a link to this thread as providing answers to today's question.
Since this thread is still open, and likely to be linked again, I would like to correct the erroneous information provided above.
It is correct that a thief is someone who steals something.
A burglar is someone who commits the crime of burglary. The classic definition of "burglary" in the common law was "The breaking and entering the house of another in the night time, with intent to commit a felony therein, whether the felony be actually committed or not." This common law definition has often been changed by local statute over time; for example, in my own state of New York, burglary may be committed in the daytime as well as the night, it may be committed in commercial premises as well as just dwelling houses, and it may also involve entering without actually breaking in (such as entering through an open door.) The important factor is the intent of the burglar: he wants to commit a crime in the building he has entered. Now, the most common crime intended by burglars is theft -- but if a person entered your house intending to beat you up, or rape you, or vandalize your property, that would also be the intention to commit a crime, and so his action is burglary and he is a burglar. Also note that the crime does not have to be completed -- if he came into your house to steal your diamond necklace while you happened to be wearing it at the opera, and so he left without taking anything, he would not be a thief, but he would still be a burglar.
A robber is someone who commits the crime of robbery. Robbery has absolutely nothing to do with whether things were stolen from banks or shops. Instead, the common law definition of robbery was "the felonious and violent taking of any money or goods from the person of another, putting him in fear." Again, this definition has been changed by local statues, but the general concept is that robbery is the taking of the property of another with the intent of stealing it, and that taking is accomplished through the use either of force or the threat of force. A person who steals a wristwatch from a shop by slipping it into his pocket and walking out is a thief, and a shoplifter, but not a robber. On the other hand, a person who comes up to you on the street, displays a knife and threatens you with it unless you give him your wristwatch, and then runs away with the watch, is definitely a robber. The reason that one speaks of people who rob banks is that a bank robber usually shows a weapon, or hands over a note making a threat -- and thus uses force or a threat of force in order to get the bank employee to hand over the bank's money.
