Yup, they mean the same thing. でしょう is a bit softer and is used by both men and women in polite situations. だろう isn't very polite and is most commonly used by men in informal situations. Women usually say でしょう even in informal situations. Since it has several meanings you could check out http://www.alc.co.jp/ and search for them to get lots of example sentences, and http://www.guidetojapanese.org/certainty.html for some grammar and more example sentences.

deshu is similar to english " let do something" darou is similar to english " do something"

umm, actually these are same meaning. 「かれは11時にがっこうに行くだろう」 "kare wa juuichi ji ni gakkou ni iku darou" it feels not polite. 「彼は11時に学校に行くでしょう」　is polite sentence. "kare wa juuichiji ni gakkou ni iku deshou"