Yep. Bushie is 99% there.

Pixel (density or numbers) count equates to 'resolution', or the chances of a piece of image being seen...by a pixel, or two or three or...
Noise is the (usually) undesirable side-effect of increasing sensitivity, the ASA or ISO number. It won't reduce the 'resolution' but can mask it.
-Noise is not Grain.
They are the results of totally differant phenomena, one electrical the other chemical/physical.
-Noise is sort of regular, whereas Grain is random in shape etc
-Noise is not nice to look at... well, for those of us familiar with grain, which can be aesthetically pleasing where appropriate.
-Grain cannot be easily/cheaply duplicated by software, though see the link for something that does. At a price.
A picture is worth a thousand words...
TrueGrain Overview
Hope that gives some, er, 'resolution'.
James the Luddite, still hand-developing his glass plates...
(not really)
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