Both mean reading or to read in the verbal form but in what context do you use 読み/読む and in what context to you use 読書/読書する ?
読書 is more like the hobby or activity of reading, most commonly with books.
読む is a very broad verb that means 'to read' in a literal and or metaphorical sense. You use it for books, newspapers, etc. but also for perception, like in English. E.g:空気を読む is the same as the English phrase 'to read the room'.