Bread flour has more gluten, which is a protein that makes bread stretchy and less crumbly when the dough is prepared right. There is plenty of whole wheat bread flour out there, and you can often get mixes which are specifically made for bread machines, I'd start with those and see how you go. If you cannot find them in your local store you might be able to find them online.
You can also read the label on the back of the flour, higher protein flours generally mean they have more gluten. You can sometimes find non-bread flours that have almost as much protein as those marketed as bread flours, so next time you are at the store have a look.
Flour types are quite different in various countries, but yes, all flours are basically made from crushing grains (wheat in this case).
A grain mainly consists of three parts:
Source: http://www.californiawheat.org/industry/diagram-of-wheat-kernel/
The bran.
The outer layer of the grain.
The endosperm.
The white inner part that we tend to associate with flour.
The germ.
The sprouting section. Often removed in flours for longer shelf life.
So when milling grains, the parts of the grain are separated, for whiter flour (that's the lower numbered types, the number actually giving the mineral content and indirectly indicating the fiber content.), the bran and germ are mostly removed, "brown" and "black" flour (middle to high number range) increasing amounts of the bran are kept,resulting in a higher fiber content.
Whole grain is - as the name implies - made from the whole kernel (but quite close to "black" / 1600).
As you noted, the "numbers" (= mineral content) typically sold in stores are not consistent in European countries, but the pattern is always the same. (In France, the numbers seem different, but are basically the numbers you know divided by 10.) If your recipe calls for a specfic "number", you can "mix" "lower numbered" and "higher numbered" flours to get the desired strength.
For simplicity the lighter types are sometimes labeled according to their use: Cake flour / all purpose flour / bread flour (-> increasing "numbers").
The US has a slightly different system, here flours are characterized by their protein content and labeled according to use. if I remember correctly there was some kind of "substitute chart" here, but I can't find it at the moment.
Best Answer
Mark Bittman actually includes a very handy quick-reference flour substitution table in How To Cook Everything (mine is the 10th anniversary edition, not sure if it's in previous editions). This assumes that the bread recipe calls for all-purpose flour and tells you how much you can substitute for the quantity the recipe calls for:
The reason that different types of flours substitute at different ratios is primarily due to gluten content. Breads (both quick and yeast) made with alternative flours, especially non-wheat flours, will be heavier, denser, and less elastic; the substitution ratios above are meant to provide a nice balance between the nutritional and flavor advantages of the alternative flours with the texture qualities of all-purpose flour. For more information about the specific properties of each type of flour listed here, see the section called "The Basics of Flour" in How to Cook Everything (p. 835-838 in the 10th Anniversary ed.)
Note: These substitutions are specifically for breads, where you want a sturdy, elastic structure. Low-protein or low-gluten flours may substitute at different ratios in other types of baked goods like desserts where you want a finer, more tender crumb. But I didn't get into that since the question was specifically about bread.