16bit normal map means it can store more nuanced colors, translating into smoother transitions between angles (resolution allowing), or more accurate angles/normals are needed. You should consider this for baking when the contrast and range is great. If you have already a normal map which you are adding small detail bumps to and what you export to only support a single normal map, that’s the way to go. Otherwise, I’d stick to 8bit normal maps where possible, and add additional details through detail maps.
Diffuse map is an older term for the colors that go into a diffuse shader. Diffuse shader defines what colors are absorbed and bounces around for a bit inside the medium (not for real), and transmits back out but now in completely random directions (not going into O-N shading here). It’s the map you would plug into a diffuse shader in Cycles. The idea of not having lighting information in the diffuse channel (for a lighting driven clean model) is not that new, most diffuse maps will also contain specular lighting information. Especially if based on photos where this is hard to get rid of. The thing we didn’t care much about prior to PBR, was that the diffuse maps was never properly normalized to a specific norm. So we could have snow in the 0.1-0.2 range and stucco in the 0.8-1.0 range - you could deal with it using a diffuse multiplier and scene specific lighting, but it was hard to make an asset made this way work under different lighting conditions (together with other assets which might have their own wrong value ranges).
Albedo maps is similar to diffuse maps, but you’re now supposed to use maps with no lighting information. However, in addition to the diffuse reflectence, they also contain the specular color which shows up when metallic is used. Albedo maps are very hard to obtain from photographs as they contain light pollution from being a photo in the first place. I’ve seen attempts to get rid of lighting info by using a standard diffuse map going through some photoshop filters (even on hard shadow brick walls for heavens sake), but I don’t like these results. But sometimes it can’t be avoided. This “fakery” may get noticed by hardcore render guys, but it’s not that of a big deal if you avoid the obvious such as lighting a brick wall from below when there is already a shadow below it. For home rendering and generic art stuff, I wouldn’t pay too much attention to it. If you create assets for games, it’s a lot more important as the eyes putting the asset under observation will know what to look for. Albedo maps should also be normalized to a norm. Meaning that you should always keep the brightness within plausible ranges for that material by looking up albedo cheat sheets.
Note that because diffuse maps “tend to” include lighting information, they also usually look way better than albedo maps. Diffuse maps are often full range with tons of contrast and saturation, whereas albedo maps are crushed in contrast to stay within plausible range for the material. If it looks bad, it’s probably an albedo map 
Albedo maps are best produced in texturing software.
AO Maps (ambient occlusion) isn’t “supported” by Blender. If you simply multiply the albedo map with the AO map, you’re also darkening the areas that are lit by direct light when it should only darken the effect from the ambient (reach everywhere) light. If I’m struggling with getting contact shadows (although I’m not into artsy renders) and I can’t be bothered fixing the lighting/GI setup, I wouldn’t hesitate to break this “rule” if I felt it improved things. Another trick is to use it to reduce specular in those “hard to reach” places on metals.
Height map can be both bumpmaps or displacement maps. Displacement maps are usually soft in appearance, if it is too detailed with too much contrast I’d use it as a bump map. Note that, at least currently, bump maps does not disturb shadows. And similar to normal maps, can cause polished specular rays to go “inside” the object producing a black result (making me wish we had a termination shader).
Metalness map should be black or white, with grey scale values coming mostly from any antialiasing in the texture. If you need dielectric paint on a metallic surface, you generally setup paint and metallic as two shaders and mix between them when you can.
Normal vs bump; you can make a flat surface point at an angle using a single color as a normal, whereas a bumpmap would need a continuous gradient making it more resolution and bit depth dependent. In Cycles, bump maps really shines when using procedural generators for generic stuff. For specific stuff, you’re better off creating normal maps in a texture generator package as Blender can get really tricky (often outright impossible) to do texture control.
Specular maps should be looked at before using them. Use them if they appear to provide that “artistic control” for slight variation, or if the map is supposed to control fake shadow gaps when such geometry is not expected to exist. Normally the value should be around 0.5, full black for shadow gaps to avoid any specular shading to take place in the gap. I would get suspicious about any full range specular maps.
You have to look at and understand the maps intent, there are so many naming conventions and different tech being supported by various engines, there is really no “just plug it in here because of the name and hope for the best” solution.
This really brings some light into the hole texture topic for me!! Thanks for sharing your knowledge and all the links!!