A 'band' refers to a single layer for a possibly multi-layer file. Most RasterLayer objects will refer to files with a single layer.
The term 'band' is frequently used in remote sensing to refer to a variable (layer) in a multi-variable dataset as these variables typically reperesent reflection in different bandwidths in the electromagnetic spectrum. But in that context, bands could be stored in a single or in separate files. In the context of the raster package, the term band is equivalent to a layer in a raster file.
nbands
returns the number of bands of the file that a RasterLayer points to (and 1 if it does not point at any file). This functions also works for a RasterStack for which it is equivalent to nlayers
.
band
returns the specific band the RasterLayer refers to (1 if the RasterLayer points at single layer file or does not point at any file).