Nice summary Rosie C! I may add to the regular/macro difference, that the macro can focus closer, but is also optimized for closer distances. OK backing up a bit.
Any lens performs better/worse at certain settings, but there is only one setting, where the lens performs best. One such setting is focus (= distance at which image is sharp). A regular lens is optimized to perform best at infinity focus (or very nearby, say hyperfocal distance at largest opening). You can focus the lens to a closer distance, but some lens errors will creep in (loss of resolution, chromatic aberration, spherical aberration, lateral color, coma, ...).
A macro lens is optimized for closer distances, usually around 1:10 magnification. You can still take images at infinity, but the images will be worse than with a normal lens of same quality. Various macro lenses are optimized for different magnification, but even typical macro lenses are not optimized for 1:1. The old Olympus 80 mm bellows head lens was an odd one, as was only for magnifications of 1:2 to 2:1 (with supplementary lens). The Canon MPE 65 mm is another specialty lens going from 1:1 to 5:1, with TC to 7:1 or even 10:1.
Re quality of extension rings, true extension rings don't have any lens elements in them (there are some macro-teleconverters, but would not recommend them). The important part is how well the extension ring mates with lens and body, how much (or rather little) wiggle room/play there is between the components. You can put body and lens with a collar on a rail to counteract any play. The other question is, how much worse are the above lens errors being made? As discussed above, the further you get from the optimum setting, the worse the lens errors get. If you add an extension ring to a poor telephoto lens, the chromatic aberrations will get much more pronounced.
That is why I wonder in my previous posts, what is better: a top notch 300 mm f/2.8 lens focused opposite to where its optimum lies and amplifying that error with an extension tube? Or, take a not quite as good a lens (Sigma 180 mm macro) but use it close to its optimum setting?
Re full-size/DX-APS-C format, the sensors are larger (yes, full-size = old film SLR size = 24x36 mm), and you can actually capture the full resolution of a high quality lens. The number of megapixels is not defining resolution, contrary to what most people think. Resolution is measured in line pairs per mm. You can fit more line pairs on a larger sensor. So the larger the sensor, the greater the potential information you can gather. On small sensors, you may get many pixels, but they only show very detailed blur, but do not convey any image information. The weakest link is the lens, so rather get a good lens and a mid level body, than the other way around.
Second, at same MP count, pixel size is larger on an overall larger sensor, so low light performance is better (less noise).
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