loss-full compression work on the same principal of replacing larger patterns with smaller patterns, using a structure, to translate one from the other. However freed from the constraint of having to recreate the original, the compression can be more effective. It uses the principle that certain difference are indistinguishable to the eye to be more effective in this replacement, however it is not perfect and sometimes the eye can distinguish the difference, hence the artefacts.
Banding has nothing to with jpeg. It is caused by using too small a bit depth for the task at hand. 8 Bit with gamma encoding is right on the visual threshold that is required for display on a computer monitor. i.e. there is not much additional room for tonal expansion. An 8 bit file saved with a linear encoding will cause banding.