I think, that those are 3 different axes, but many times commited in combination.
- Thief - get something, what is not his/her.
- Robber - attack or threat with violence a person (with intent usually to get something)
- Burglar - breaks to house (with intent to rob or steal)
But there may be situations ... say I travel by train far away, went asleap and Thief got all my lugages, wallet, clock and jewelry.
I woke in some town with nothing, just clothes, then in dark corner was attacked by Robber saying "money or life" while poiniting gun at me - I told him my story and showed him, there is nothing to get, so he mutter "your clothes sinks and ammo is expensive, run away and do not show again" - it was totally Robbery, but he did not steal anything (so not Thief).
More over Burglar went to my old flat by climbing wall, broking window and kicking down doors, just to see, that there is nothing inside, because I moved few days ago, taking everything (include light bulbs) to my new house. It was burglary for sure, but again, he did not steal anything, as there was nothing of value inside. (Not Thief or Robber)
While he was looking for anything valuable, another Burglar went in and seeing his bag and hammer lying near my door, he Steal it (so this one was also a Thief but not Robber) and then sneaked away.
To be it more complicated, even another Burglar went then inside and seeing the first one still searching, he put out a gun and Robbed the first of his pocket money and hand lamp (so this one was Burglar, Robber and Thief at that time)
Have I to add next one to his misery, who is Burglar and Robber, but not Thief?
Well on other note if somebody make more wrongs at the same time, it is usual to call him mainly by the most serious crime he does. Those less serious may be cited too with the main, but rarely they are mentioned just alone.
Say a mad man broke in some house at night, splash gasolin all over and light it, so the house was burned to the ground. On the way out he took pack of cigaretes from table and smoked it, while going home. We will call him Arsonist, maybe add Burglar.
To say about him just "He is Thief" does not sound right, even if he took those cigaretes.