It's the 2011 net animation series by Gainax that was eventually remade as a full TV series in 2015. It's lovely and really good, but also so similar to the 2015 that there's not much point in watching both. Just watch the full-length one. The 2011 series immediately gets everything so right that there was no need to change anything. The designs are the same. The cast are all identical in character design, personality and voice actor. The plot's the same, except shorter. Watching both versions doesn't give you a different take on the story, but instead just a repeat of exactly the same show.
The only difference is its length. All four mini-episodes watched back-to-back run exactly as long as a standard anime episode. (If you're watching on the show's official YouTube channel, this is easy. YouTube will by default play ep.2 after you've finished ep.1, and so on.) More precisely, the episodes' lengths are 6:07, 5:01, 5:30 and 7:16.
It's thus still the story of Subaru, who doesn't know she's about to become a magical girl. Her friends will be Aoi, Itsuki, Hikaru and Nanako, while their antagonist will be Minato. Yes, Subaru first meets him in a magical greenhouse. Everyone's the same as before. They say and do the same things, although I liked the effect of condensing the action. I prefer this take on the Subaru-Aoi relationship, for instance. We don't get a mundane scene of the two of them walking to school at the beginning, which turns out to have been unnecessary because their first 2011 scene is a lovely bit of storytelling, simply and clearly telling you everything you need to know. (I like that 2015 mundane scene too, but it's interesting to see how well the story works without it.) Similarly, every Subaru-Aoi interaction is more important here (due to this version's greater density) and I think their relationship is clearer for not having to foreshadow the 2015's finale.
One trivial difference is the girls' magical sky pentagram in ep.3. Here it looks like a satanist symbol, whereas the 2015 softened that with lots of circles. Also, importantly, the 2011 series doesn't really have an ending. It ties everything up in the short-term quite nicely and it's all very enjoyable, but then it just stops and you'll be left wondering when the next episode's coming out. (Answer: in 2015.) That's a mild Gainax ending, although nowhere near as confusing as their most notorious examples.
It's adorable, of course. It looks just as beautiful as its successor, especially its colour palette. It's a delightful piece of work, but these days I think its most useful role might to be a sampler for people who might like the full-length show but are more likely to make time to watch something short like this.