A Retweet is defined in two ways: an "official" Retweet, done through the Twitter button, or through Twitter's apps. The other is defined as those Tweets which contain the "RT @username" structure and reference part of the Tweet retweeted.
You mention that you get totally different results from other websites. Could you possibly send an email to firstname.lastname@example.org explaining that in some more detail. We're always curious to know whether we can improved our service in some way.