OK, point #1: They did that wrong. Seriously.
Well. I suppose it might actually be strong enough. But that is really, really, not the proper way to hang steps.
Back to that in a minute. As to your question about the board sizes. This is in part a historical accident, and in part a cost saving measure. Back in the day, a 2x4 (6,8,10,12, whatever) was in fact that dimension. But they were rough cut. That is, cut with a course saw, and not smoothed down. Then they came up with what they called planed dimensional lumber. That is, you start with a 2x4, and you run it through a machine called a planer and it came out fairly smooth. But it came out with a dimensions of 1.5 inches by 3.5 inches. Later on, they switched to smoother saws, and just cut the boards to 1.5x3.5. But they retained the names of 2x4. That is, you're converting from metric, so it seems screwy to you. But to Americans, when buying a 2x4, we know we are getting 1.5x3.5. That's just the way the wood is cut. They do it because they get more boards out of each tree.
So if you ask for a 2x4, you will get a 1.5x3.5. If you ask for a 2x12, you will get a 1.5x11.5. This holds true for all dimensional or framing lumber on the US, and probably Canadian, market. That includes pressure treated lumber.
Now, clearly I have not confused you enough. So just to make things interesting, plywood is different. And plywood is labeled as exactly the dimensions that the wood actually is. That is, it is mostly sold as 4x8 sheets, and that is pretty close to exactly on 4 feet by 8 feet dimensions. And the thickness of the sheets will be extremely close to the labeled thickness as well. The other major exceptions you'll find is finish grade lumber, which they are now selling as exactly the labeled dimensions as well. Also molding carved lumber tends to be exact dimensions as well.
Tradition, were would we be without it?
Now, back to our regularly scheduled program. The decking boards that you measured at 1 inch are actually called 5/4. That is, 5 quarters. (The logic is the same as above. Just go with it. Thinking about it any further will just give you a headache.) It's a commonly used size for the flooring on a deck. It's normally sold with a somewhat better grade of surface smoothness than 2x lumber. It makes for better appearance for flooring. But I wouldn't use it for a step. Just to finish out your education here, dimensional or PT boards that are called 1x, that is 1x3, 1x6, ect, are actually .75x2.5, .75x5.5, ect.
So the boards you want to ask for are either 2x6s or 2x12s, and they will be 1.5inches thick.
Now, to the brackets, well I suppose you can make a case for them being good enough. Take out the screws that go to the step boards, and you can reuse them.