it took me ages, actually, make that years, to figure this out. it wasn't until i started making knives that it finally made sense.
essentially sharpening is about 3 things; the intended use of the blade (wether its an axe, saw, knife, plane, or chisel the same thing applies) which is the action of the cut (sawing, chopping, hewing, pairing/slicing);
the density/hardness of the material to be cut vs the hardness of your tools cutting edge;
and the angle of entry of the blade.
these inter-dependant things govern the angle you need to sharpen your tool at.
the angles quoted are the angle from the outside face of the blade that you sharpen to the centre of the blade.
different blades will cut differently, for different uses, and its hard to achieve an all round tool that works well in all situations. which is why, for instance, you may find it hard to make feather sticks for fire lighting with a hunting type knife, however sharp it is, because the shape of the leading edge of the blade is wrong. this is how we all end up with a shed load of tools. flat and hollow ground blades allow you to pair things more easily than convex ground which allows you to chop more easily.
although the exact angle you use to sharpen isnt entirely critical, it can fall well within a range (generally 12.5 -30 degrees), the consistency of maintaining the same angle is more important, honing guides help, but theres a point where you will have to go freestyle, because not everything fits in a honing guide, axes and knives esp.
its a thing where you have to spend an amount of time to get it to run right. if you use a mechanical sharpener, like a grinder you need to be really careful you dont heat the edge of the blade, or you will remove the temper from it and it will require you to grind out the whole area you've cooked or you will keep chipping the edge. tomak water wheels are a way to go, but its not so difficult to sharpen by hand.
the angle plane blades are set in the body of the plane determines to an extent the angle the blade needs to be sharpened at (generally 25 degrees) you can get away with putting a micro bevel on a blade, but only for so long before the micro bevel is too large and begins to hinder the process of cutting. they are a good way of avoiding having to sharpen the entire face of the cutting part of the blade, but you can only do that for so long before you have to completely re-grind the face. the same with chisels.
25 degrees will give you a finer point of entry which allows you to pair things, and 30 degrees will give you a better chopping edge.
too fine an angle of entry is counter productive for chopping blades as it causes them to stick, yet conversely, to pair something, the finer the angle the finer you can shave things.
the key to successfully sharpen double bevelled blades is to try and remember to count how many times you run it over the sharpening stone per face, and make sure its an even amount each side.
hope it helps
rick