Crime
In ordinary language, a crime is an unlawful act punishable by a state or other authority. The term "crime" does not, in modern criminal law, have any simple and universally accepted definition, though statutory definitions have been provided for certain purposes. The most popular view is that crime is a category created by law; in other words, something is a crime if declared as such by the relevant and applicable law. One proposed definition is that a crime or offence (or criminal offence) is an act harmful not only to some individual but also to a community, society or the state ("a public wrong"). Such acts are forbidden and punishable by law.
Terrorism
Terrorism is, in the broadest sense, the use of intentionally indiscriminate violence as a means to create terror among masses of people; or fear to achieve a financial, political, religious or ideological aim. It is used in this regard primarily to refer to violence against peacetime targets or in war against non-combatants. The terms "terrorist" and "terrorism" originated during the French Revolution of the late 18th century but gained mainstream popularity during the U.S. Presidency of Ronald Reagan (1981–89) after the 1983 Beirut barracks bombings and again after the attacks on New York City and Washington, D.C. in September 2001 and on Bali in October 2002.
Terrorism
No-one becomes a terrorist from a standing start. It starts with a process of radicalisation. When you look in detail at the backgrounds of those convicted of terrorist offences, it is clear that many of them were first influenced by what some would call non-violent extremists.
David Cameron, speech at Ninestiles School, Birmingham. (transcript by The Independent)