A parallel world type is a mixture of reality and fantasy. The real world exists, but there is a parallel fantasy world that exists as well. The most famous example as got to be Harry Potter. While urban fantasy can be entirely fantasy, a lot of examples of having a fantasy world parallel to the real world can be found in books such as Neil Gaiman’s Neverwhere, Benedict Jacka’s ‘Alex Verus’ Series and Ben Aaronovitch’s crime/fantasy series involving PC/Wizard Apprentice Peter Grant.
In all of the examples above there is a parallel magical world that exists, usually concealed from the majority in the real world, but that does have an effect on the real world. Think about the opening chapter of ‘Harry Potter and the Philosopher’s Stone’ where Vernon Dursley see lots of people in cloaks, gets called a muggle and the new reports in the evening talk about unusual owl activity. All because Harry lived and Voldemort ‘died’, the wizarding world was active enough to be noticeable to the muggle world. Normally, unless they knew, most muggles don’t know about the wizarding world.
The trick with building a fantasy world and running it parallel to the real world is having a very good understanding of both the reality you’re using and the fantasy you are building, and then also how they are integrated and separated from each other. J.K. Rowling was particularly imaginative in creating places like Diagon Alley and Platform 9 3/4s, which are based in London but are also separated from the real world entirely.
In ‘Neverwhere’ by Neil Gaiman, the magical almost sub-world of London, has wonderful dark twists of wordplay and imaginative creation for Richard Mayhew to explore as he tries to find a way to be part of the real world again.
Creating a parallel world type is in the most part not that much different than building a fantasy world, but you do also have to take into considerations of the real world, whether in the past or the present. You can also build a parallel world into a Future Reality world type as well, which I will talk about more in the post dedicated to that world type. The main thing to remember to know the boundaries between the worlds and where those boundaries are sometimes broken or even if they get broken at all.