Sheet metal is just what is says....a sheet of metal. You can get most metals is most ways, which is.....sheet, plate, bar, or tube. Then you have the different processes, which is hot rolled, cold rolled, extruded, cast, forged, and so on.
Normally the difference between sheet and plate, is the thickness. Some of that will depend on the manufacturer where they want to make the dividing line at. Some will say that a 4'x8'x.125 thick is a piece of sheet metal, and may call a piece of 4'x'8'x.187 a plate. I have always used 1/4" as sort of the dividing line between sheet and plate, when ordering material, and found it in a lot of catalogs the same way. And some of it also depends on how it comes from the manufacturer. There is not really a cut in stone dividing line on where sheet stops and plate starts. A lot of times, sheet will not be called out in thickness like 1/16", 3/32" but instead will be classified in Gage sizes like 26 Ga., 16 Ga., and so on.
about the best way to find out where the differences separate is go to a site for materials, say like Central Steel & Wire, or Copper & Brass, and see how the materials are listed.
Ideally, if you want to find out about materials and their differences, there are a lot of website places if you do a search, you have your local library, you can always spend $50 and pick up a Machinery Handbook which will have more information that your brain will ever hold, or pick up a magazine like Home Shop Machinist, the Machinist Workshop, and look at some of the many publications they advertise in the backs of them. Plus the articles are pretty good also.
But to just ask for clarification of metal types, covers a very, very, broad field. It's not as simple as a one or two paragraph explanation, unless you just want to know what your tool box is most likely made FROM. But to explain material differences covers a lot, and the best thing to do is just start reading different machining books, magazines, and websites, then when you read something and have a question on the terminology, just do a search to see where that leads you.
And don't take it wrong, I'm not trying to discourage you on here, but there is a lot to know, and too much to type out unless it was for something specific.
Ad far as your particular toolbox, it can be answered simply as the box is most likely made out of 1018 Cold rolled sheet metal of whatever thickness it is. Or to sound more technical, it is made of a low carbon sheet steel. And to expand on that, it was die formed from a piece of low carbon 1018 steel sheet.
A simple piece of metal can take many forms (no pun intended) depending on who you ask and how simple or complicated of an answer you want.
Great advice and explanations gentlemen!