TNT is indeed a very safe explosive. And yes, it burns ~like wax, but lots more sooty. Basically, detonation requires high-velocity shock. More even than blasting caps. You need a secondary explosive. Which, anyway, is why it's good for artillery shells.
Belated footnote: When the military run low on TNT and other "safe" explosives, sometimes they switch to stuff that's far more shock-sensitive, ages faster, and becomes very hazardous over time. So one key thing is knowing which types of munitions are ~safe to play with, and which are deadly.
Also, TNT releases NO2 when it burns (or detonates). Plus a bunch of ~toxic and ~mutagenic aromatic hydrocarbons, which end up absorbed on the soot. Some of which is respirable.
