Before you consider reading "Mahou Shoujo Madoka★Magica: The Different Story". It is highly recommended that you either watch the original anime series or read the manga adaptation (both called Mahou Shoujo Madoka★Magica) due to the Different Story not only referencing events from the original but it was pretty much written under the premise that the reader has seen the original.
That said I will keep spoilers to a minimum for both the original and Different Story so both people who are familiar with the original series and those who aren't can still read this review.
Now onto the actual review:
Mahou Shoujo Madoka★Magica: The Different Story is actually BOTH a prequel and alternative universe of the popular Mahou Shoujo Madoka★Magica series.
The premise of both Madoka Magica and the The Different Story is pretty much a darker take on a "Magical Girl" setting. If you've seen or read a magical girl series like Cardcaptor Sakura, Sailor Moon or Precure you know magical girl series are usually happy/optimistic series with tons of friendship/love speeches aimed at kids (not this is a bad thing).
The Different Story takes a darker and somewhat more realistic approach on the genre, with the big question being.. "Is it really ok to take on the responsibility becoming a magical girl just for one wish?"
Despite the fact that this manga is called MADOKA Magica, the title character Madoka Kanme is only a minor character in the Different Story. The actual main character is Mami Tomoe, a character who only got a little bit of screentime in the original series.
The art style in this series is very good and detailed. It comes very close to the style of the original series. The action scenes are decently detailed for a manga though not quite as good as they are done in the original anime.
The first 4 chapters serve as a prequel to both the original series and the rest of "the Different Story". Mami Tomoe is a somewhat experienced magical girl yet keeps it a secret from all her friends at school. When not at school she tends to be a bit lonely.
That all changes when she meets Kyouko Sakura, someone who has just recently made a contract to become a magical girl. Kyouko is quite inexperienced with fighting so Mami gives her advice to defeat the witch (the "enemies" of this series) she was fighting and helps her defeat it. After that they become friends and begin to fight alongside each other. However, after a while certain complications begin to rise and the story really starts to kick in.
The rest of the series mostly explores Mami Tomoe's character answering questions like "What does she really fight for?". Kyouko Sakura also gets a bit of development but not quite as much as Mami.
There are 4 other characters who are quite minor compared to the Mami and Kyouko but still play a decent part of the series. Sayaka Miki and Homura Akemi are magical girls who appear later on in the story. Madoka Kaname, the title chraracter is someone who is deciding whether she wants to be a magical girl or not. Kyuubey is a little cat-like creature who gives girls the power to become magical girls.
The rest of the story is a bit hard to explain without spoilers but if you're really interested to see a more unique take on a magical girl series that explores bonds with others on a somewhat deeper level than most of the genre then you should definitely check this manga out.
For those who have seen/read the original series and either:
A) Wanted more of Mami and Kyouko
B) Want more of the Madoka Magica series in general
then you should most definitely give this manga a try.