tome, counter for books, volume
冊 centers on bound written material: a tome, a volume, or the counter used for books and similar bound items.
冊 is a pictograph of bound bamboo or wooden slips used for writing in ancient times. The vertical strokes represent the individual slips, and the horizontal strokes represent the binding cords.
The vertical lines are the pages or slips, and the horizontal lines are the binding. Picture a stack of bound bamboo slips forming a book: 冊 is a tome or volume.
For サツ, imagine a stack of books sitting on a shelf: the word 'sats' sounds like 'sats' in 'satsuma', but more directly, think of a 'satsu' as a bound volume, and the reading サツ is the first part of 'satsu'.
counter for books
book; booklet; story book; pamphlet; notebook
separate volume; extra issue; supplement; additional volume; supplementary volume
separate volume; fascicle; fascicule
tanzaku; poem slip; poetry slip; long, narrow strip of paper on which Japanese poems are written (vertically)
number of books
one copy (of a book, magazine, etc.); one volume
imperial edict to confer nobility titles (in ancient China)
bound form (of a magazine or book; as opposed to a single sheet, scroll, etc.)
bound book
printed edition (as opposed to digital)
bestowing peerage by imperial edict (in ancient China); document bestowing peerage
tributary system (of Imperial China)
accredited Chinese envoy to neighbouring kingdoms
imperial investiture; installation
separate-volume supplement (to)
each book (volume or copy)
collection in one volume
large or bulky book or volume
pamphlet; booklet