Numerically, bump and displacement mean exactly the same thing. They differ in implementation.

Assuming we're dealing only with Poser (and not other apps) and that users know how Poser shaders work, these two maps differ in overall height. The brighter one means to generally be higher than the darker one.

However, there's a metric ton of Poser users who don't understand either the maps, the math, or how you would properly go about making these.

You may be asking too much of me to tell you what they (people who made those maps) intended, since it is highly likely they have no idea what they said.

If they made the maps from gray-scaling the color map, they are clueless and the maps don't mean anything at all.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)