Judging by the nutrition information I can easily find (for example, from nutritiondata.self.com), frozen spinach is generally cooked by boiling and draining. That's pretty much what I'd have guessed; it's certainly the easy way to cook things.
Unfortunately, that means that some nutrients are lost with the discarded water. I doubt it'd be different for any other green leafy vegetable - though it's certainly much harder to find frozen mustard greens!
The nutrition information for fresh spinach is for fresh, raw spinach; if you boiled and drained it, you'd make the same sacrifice that the frozen spinach has.
As for your generalization, freezing vegetables and fruits does preserve most things pretty well - but only what's actually left in them when they get frozen! And while transporting fresh vegetables around can cost you some "freshness", it's not going to affect minerals. Some vitamins could be lost by breaking down (I'm not an expert here, but it seems possible) since they're more complex molecules, but minerals are just single elements. Those iron atoms won't fall out of the spinach on the way, and they're certainly not going to be transmuted, either!
Edit: Essentially what's been said in the comments is that the USDA nutrition facts say that "Spinach, frozen, chopped or leaf, cooked, boiled, drained" has about half as much iron as "Spinach, cooked, boiled, drained". A discrepancy, indeed, though not the same one cited in the question. My interpretation here is that the frozen spinach is simply not cooked in the same way (boiled and drained more thoroughly) as the non-frozen.
An alternative, proposed by Adisak, is that the frozen spinach nutrition means that you've taken the already-cooked, frozen spinach and boiled it again and drained away even more nutrients. This seems unlikely; frozen spinach is already cooked, so there's no reason for the nutrition information to assume that you'll boil it over again. The description (it seems to me) is referring to the cooking that took place before it was frozen.
Frozen spinach has been boiled/blanched. You can do this if you really want it to be as much like frozen spinach as possible, but really, you can just cook it with the water left on the leaves from washing - effectively a bit more like steaming. There's no need to freeze it. This will result in something with fresher flavor and a bit more substantial texture than frozen spinach (not as eager to disintegrate). And you don't have to worry about moisture much - a lot of the water will cook off - but you can certainly drain it additionally if it's too much for you.
If you really want it exactly like frozen spinach, you could boil it, and maybe even freeze it to help mess up the texture, but I'm guessing you'd prefer cooked fresh spinach anyway. In this case, you'd have to squeeze and drain it just like with frozen spinach to get the water out. (If it's unclear how to do this, see What is the most efficient way to squeeze water out of cooked spinach?.)
Based on nutrition facts for raw spinach and frozen spinach, one 10 ounce package is approximately the amount you'll get from cooking a 340g (12 ounce) bunch of spinach - that weight is probably after removing the stems you're not actually going to cook, though. This fits with my experience cooking down spinach. Most things you'll use it in are really forgiving, so probably best to err on the larger side with your bunch of spinach!
Best Answer
Before being cooked, vegetables are like a wall built from tightly filled water balloons. Each cell has is filled with water (well, technically cytoplasm, but...) which is essentially incompressible.
One of the components in the cell walls is hemi-cellulose, which dissolves into the water when the vegetable is cooked. This allows the individual cells to partially deflate, expressing water and making the overall vegetable wilt.
Think a blown up beach ball. Although the wall is soft and flexible, the air holds it rigid. Of course, air can be compressed, so a beach ball can be squeezed; but water for all practical purposes is not compressible, so there is no almost no give in the individual plant cells.
Once the cell walls loose their integrity, however, it is like the beach balls that comprise the plant have sprung a leak. They loose their shape or rigor, and at the large scale you see wilting or softening.
Note that the presence of acid in the cooking medium can inhibit the dissolving of the hemi-cellulose, and permitting vegetables to better maintain their shape. This is one reason why, for example, canned vegetables have acid added to the canning liquid (another being that acidity above a certain threshold inhibits the growth of certain dangerous food born pathogens.)