I think Som’s answer may relate to British English. In American English, “notorious” means famous (i.e. well known) for something bad. A “common criminal” is an ordinary criminal with nothing special, as opposed to a celebrity criminal (a famous person who commits a crime), a super-criminal (like those faced by super-heroes), a notorious criminal, a Robin-Hood (steals from the rich and gives to the poor), a criminal genius, etc. “Common criminal” is a collocation, whereas “ordinary criminal” is merely an ad-hoc combination of an adjective and a noun. To call someone a common criminal is a huge insult, since it suggests that he is not even outstanding as a criminal.

I agree with Phil. In the US anyway (and speaking as a lawyer) people who are convicted of felonies or misdemeanors are frequently called „common criminals.“ it’s got nothing to do with misdemeanor vs. felony classification. A common criminal is not a legal phrase, but my perception of one would be that of a non-violent offender (a petty thief perhaps, embezzler) as opposed to say a rapist. You wouldn’t call a rapist a common criminal, you’d call him a violent offender.

An „ordinary criminal“ I suppose would be synonymous with a common criminal but I’ve only rarely heard that phrase used.

A notorious criminal would just be someone everyone has heard about, at least in one country anyway. In the US for example, Charlie Manson, a well-known murderer, was a notorious criminal because his name here was practically a household word. He garnered tremendous publicity over the last 50 years. In Germany, Andreas Baader and Ulrike Meinhof were notorious criminals in the 1970s because they were part of a terrorist organization, the RAF.

Phil's answer also applies to British English. A common criminal is a frequent offender who is not particularly famous, inventive or outstanding in the field of crime and is a collocation. A notorious criminal is famous for their crime. Perhaps Som's reply is more about Indian English, which is a major variety of English in its own right, and probably, in terms of numbers if speakers, the most common.

Precisely, Phil. As in "Sir Isaac Newton was famous for his scientific genius but also notorious for his unpleasant temperament".

There is no literal interpretation of this term because people often use it very loosely. In legal terms common crime can be:

1. A misdemeanor as opposed to a felony.

2. Crimes (arbitrarily) listed under common law.

3. Most frequently or commonly committed crimes.

Since even the legal definitions do not coincide, lay usage is even more arbitrary based on what an individual thinks a common criminal is.