The division between 'tactical' and 'strategic' nuclear weapons is a bit of a joke in the military and its associated industries. Really, the difference hinges not on what the weapon looks like, how it's stored, who made it, what color it is, how big it is, or even how it's fired or who has authority for it. The true difference lies in what the weapon is launched at. For example, a 60 kt Trident II missile RV, considered 'strategic' by most lights, doesn't really have a 'strategic impact' if it's dropped on, say, a couple of divisions of armor in the Iraqi desert. (Okay, okay, no first use policy and 'breaking the nuclear barrier' arguments aside). Comparatively, a 0.5kt device, if detonated (say) under the Pentagon by a non-U.S. government is extremely strategic. (if it's a U.S. Government, like, say, that of Texas, well then that's a whole different story :-/ :-P)

Facetiousness aside, the typical means of classifying these things is to determine if it (in its deployed, designed form) falls under the rubric of a 'strategic arms' treaty like SALT or START. If it does, then whoopee, it's not a TNW. This in itself is a bit artificial because START (for example) is concerned with launchers, not warheads.