What they said.

Sometimes finding the right spindle can be frustrating. The width of the BB shell dictates the distance between bearing races so most any British (non-Italian) width should do. But the required length depends on the shape of the crank arms and how far outboard the ring mounting is w.r.t. the spindle hole. Different cranks could be 10mm or even 15mm different. Your spindle can be a mm or even 2mm off from the spec as long as the small ring doesn't hit the frame. After all, you will run different gear combinations and only two combinations will have perfect chain line; all the other combinations will be offline to some degree. But you don't want it so far off on the combinations you stay in most, and you don't want to pair up extremes, as say, a 115mm spindle with a crank that wants 103mm.

The taper is another issue that could be problematic but usually isn't. Almost all road cranks are 4 degrees, but the width between the faces is different between JIS and ISO. (IIRC, ISO is slightly smaller.) It is a taper, so a smaller width means the spindle will fit further into the hole. That affects the chain line. The more significant issue is that if the spindle is too small the cranks arm could bump up against the shoulder of the taper at the inner end instead of sitting flush with the taper faces. Also if the spindle protrudes past the hole's edge enough the crank bolt or nut hits the spindle and not the crank arm. But if the spindle is too large the crank arm won't engage the taper fully before bottoming out. This latter case is more of a problem if you are really strong and heavy and mash the pedals hard, in which case it could stress the hole.