This is a problem fraught issue. 9/11 prompted a determined but it now appears ultimately unsuccessful widespread international effort to define terrorism. For an excellent summary, see http://en.wikipedia.org/wiki/Terrorism_(definitions_of)
Having said that, I would argue that current usage (note, not WWII) in practice (amongst Western militaries at any rate) differentiates more-or-less as follows (source: my professional experience, particularly in Afghanistan, summarized off the top of my head):
Terrorism: attack on civilians meant to terrorise them in order to further a political agenda. Illegal under the terms of both criminal law and the law of armed conflict. Think bombs set off in public places by "cells" of persons hiding amongst the populace (ie not openly bearing arms).
Insurgency: covert attack on the organs of government authority in attempt to overthrow said government. Almost certainly illegal under the local criminal law, but not *NECESSARILY* illegal under the law of armed conflict. Think ambushes of government troops out in the countryside by armed bands.
Note that insurgents can (in principle at least) conduct themselves in accordance with the law of armed conflict (if they openly bear arms, and discriminate in their attacks, targeting only government armed forces), whereas terrorists are illegal under every legal regime (hence the intense argument as to what makes one a terrorist). In practice, however, insurgencies often make use of "terrorist" tactics, as well as what one might call "guerrilla" tactics. For example, the Taliban in Afghanistan tend to have bands of armed men out in the hills, who fight the government and ISAF troops, more-or-less in the style of the classic "mujahedin"; as well as "terrorist" type cells of covert actors in towns, bombing, assassinating, and dropping what we called "night letters" amongst the local populace. The two groups are clearly not water-tight compartments, but (I would argue) they are reasonably distinct.
As a coda, I would argue that the term "guerillas" is generally used to refer to insurgents, often sponsored by an outside state as part of a wider armed conflict. "Partisan" is interesting in that it has essentially fallen completely out of use. Historically, it was used as a Slavic/East European term for communist sponsored or sympathetic insurgents or guerillas behind German lines. One might suspect that it is because of that communist association that the term has fallen out of use, following the fall of communism itself. See http://en.wikipedia.org/wiki/Partisan_(military)
"terrorist" = civilian on civilian attack that is not legal under the law of armed conflict or civilian criminal law; and
"insurgent"/"guerilla"/"partisan" = irregular groups, but ones who are engaged in what international law would recognize as an armed conflict, and could conduct their efforts in accordance with the law of armed conflict (if they have a recognizable organizational structure, openly bear arms, and discriminate in their attacks only against legitimate targets, i.e. armed forces)