【をお願いします】is more polite and formal then [を下さい].

Hi Jaden. I'm not fluent in Japanese as well, and am still learning my way to get a certification. But as far as I have known, both can be used to ask for help or favor. :)

Hellow,Jaden. It's a interesting question. Both 「水をおねがいします」 and 「水をください」 are the same meanings, but, in the case of 「水をお願いします」, I use it as an answer to question. For example, if you say 「ブーツを下さい」,the staff know you need boots in shoes store. If you say 「ブーツをお願いします」suddenly,the staff may not know what you need. When the staff say which do you want running shoes or boots?,「ブーツをお願いします」means "I want boots". I think that 「水をお願いします」is abbreviated way of speaking 「水の提供をお願いします」.

I agree with Marijan and Julia. :)