Kudasai is much more Concrete, and Onegaishimasu is much more Suggestive. You can say "kudasai" with a verb (-te form), but you can't say "onegaishimasu" with it. The meaning of "onegaishimasu" is little bit different from "kudasai". "onegaishimasu" means "I'm asking you for any kinds of extra services" in a shade of difference in meaning. In a bookstore, for an example, you can say both "この ほんを ください-kono hon o kudasai", and "この ほんを おねがいします-kono hon o onegaishimasu" Both literally mean "give me this book", or just "this book please" The 1st phrase simply means "this book, please" but when you use the 2nd one, you may be asking "an advance order" or somewhat in a shade, but you can say the 2nd one as just meaning "this book, please". As I show, there are different nuances. That's why, when you say "カバーおねがいします-kabaa(cover) onegaishimasu", the clerk should just put a jacket on your book.( as an extra sevice) It seldom means "please sell a book cover". "カバーください-kabaa kudasai", this phrase means "please sell a book cover", because "kabaa" is the one the speaker wants as a Concrete Object, not "to put" jacket.Though, usually he or she will do that for free. Then, "カバー して ください-kabaa shite kudasai (please put a jacket on my book)" is the same with "カバー おねがいします-kabaa onegaishimasu", because the thing he or she wants the clerk is "to put a jacket" (Concrete object is "to put a jacket") As I said above, you can use "kudasai" with a verb (-te form) like thsese below. ちょっと みて ください！chotto mite kudasai (take a look, please) ちょっと まって くださいchotto matte kudasai (wait a minute, please) You can't use the word "onegaishimasu" to say these. Anyway, coloquially they are almost the same thing !