Wa alaykum assalam.
Lol... i will explain this how i see it...
Reply w/ Quote- It takes the quote from whoevers post you click the quote button from
Multi-Quote w/ Message- You can click the Multi-Quote button and take quotes from more than one user
Quick Reply- Quick Reply button is a short cut, if you don't want/need all the pretty add-ons of a full reply or are short on time, just click the Quick Reply and the box at the very bottom with Quick Reply written on it will open up and will allow you to do all the basic functions. (plus if in the end you change your mind and want all the options of a full reply just click 'Go Advanced')