Flour is classified by two things that recipes care about: how much of the grain it contains, and how much protein it has.
Extraction and ash
European type numbers — 405, 550, 812, 1050 in Germany; 45, 55, 65 in France — measure the mineral content left after a sample is burned, which stands in for how much of the bran and germ survived milling. A higher number means more of the whole grain. The numbering systems are national, so a French 55 and a German 550 are close but not identical, and neither maps exactly onto "all-purpose".
Protein
Protein content determines how much gluten a dough can form. Bread flour sits higher, cake and pastry flour lower, all-purpose in between. This is why substituting one for another changes structure rather than only flavour, and why bread recipes specify.
Why a recipe may not travel
A recipe written for one country's flour assumes that country's protein range and milling convention. This is the most common reason a well-tested formula behaves differently elsewhere, and it is why hydration is often given as a percentage rather than in millilitres.
