My phone gives me two options when I want to retweet someone.
just retweeting a post means you send that person's tweet to your followers, as is.
You can also retweet it as a quote, referencing it, which means you are tweeting their tweet as a quote, sending from your account, not just "reflecting" their quote to your followers. Doing this allows you to add a comment to the quote, if there is room, showing your response to the quoted tweet, by referencing it. Sometimes people will put a "RT" in front to show the quoted is the tweet to which they are responding.
You can see the difference in Haley's tweets, sometimes she just retweets a post, which shows up as the original tweet, but at the bottom, will say, "retweeted by Haley Reinhart". The original tweeter's avatar will appear with the tweet.
a retweet:
Quote:Tusk @HaleysTusk Jan 6
If there was any justice, @HaleyReinhart would be invited to perform @ this event, Grammy salute to the Beatles
http://www.grammy.com/news/performers-an...es-special …
Retweeted by Haley Reinhart
Sometimes she will quote a tweet, then add a response at the end, Haley's avatar will accompany the tweet instead of the original author's avatar:
a quoted retweet:
Quote:Haley Reinhart @HaleyReinhart Jan 7
“@HaleysTusk: @SlashArmyJava @inSlashwetrust @Slash @MylesKennedy @HaleyReinhart
"Wild Horses" 
http://youtu.be/QaJx1Oinu0M ” Miss this night!!
She quotes my tweet, attributing it to me, followed by a colon, the tweet, then her response
(sometimes people put their response first
then quote the tweet)
I think the latter is just "Twitter etiquette" Some of the people I 'follow' will post tweets randomly, responding to tweets on their timeline, but not 'reply'ing to (connecting to the tweet they are replying, creating a thread) or quoting the tweet they are responding to, as above.
So when you see someone post something like, "that's terrible, why do that?" and you click it to see what they are referring. If they just posted it w/o attaching to another tweet by 'reply'ing to it, or quoting it, well then you get a disembodied tweet with no context.
quoting it gives context to your reply, although the drawback is your reply still has to fit within the restriction of 140 characters, including the ones in the tweet you quoted
