Unfortunately, I have no context, since it's a doubt that I have. I looked at the meaning in the Word Reference dictionary, but I'd like to know what makes robber and mugger different in meaning from stealer and thief.
A mugger is someone who works in the street and uses force or the threat of force to steal money, mobile phones or whatever from people.
A robber is a more general term and implies to me someone, or often one of a gang, who do things like rob banks, security vans etc (ie robbery is usually quite open and unsubtle). It can also be used as an alternative for brigand, bandit etc.
A thief is to me more someone who takes things by stealth.
Mugger does mean something specific, robber and thief are wider terms and in some cases can be used interchangeably.
There are legal definitions of robbery and theft that I forget within seconds of reading.
The OED definitions probably shed some light on this: theft: 1. The action of a thief; the felonious taking away of the personal goods of another; robbery: 1. a. The action or practice of feloniously seizing, by violence or intimidation, property belonging to another;
So a mugger is a particular type of robber.
A pick-pocket is a particular type of thief.
I will forget this distinction too, and I suspect most people outside the legal profession and those who specialise in knowing and applying such nuances of meaning don't bother with it either.
Okay, I'm going to take things from a legal point of view.
Robber: Someone who steals something by using or threatening violence.
Mugger (not a legal definition): This is more of a colloquial term - to me it suggets a theif who would "mug" or steal from someone in the street. It also suggests that they threaten or use violence.
Stealer: I have never heard this said or used by native speakers.
Thief: Someone who steals without using/threatening violence perhaps like a pickpocket.
stealer does sound weird, but I'm sure I've read (or heard) stealer of hearts somewhere (cf he/she stole my heart), so a word-association post might be useful as well. robber brings to mind places (banks, graves..) with mugger it is the street and thief reminds me of Robin Hood (Prince of Thieves) who was a bit of a mugger though but certainly not petty.