Miraheze is operated by Miraheze Limited of the United Kingdom and Wikimedia by the Wikimedia Foundation of the United States and are both governed by different policies. While Wikimedia strives to be an online repository of educational material, Miraheze's goal is to provide its users with great MediaWiki hosting for free.
Miraheze was formed by two Wikimedia users. Many of the first users on Miraheze were fellow Wikimedia users who had heard of Miraheze through other Wikimedians. Even today, many of our users also volunteer on Wikimedia projects or have a long history of previously having volunteered there. Some of our users have served or currently serve as Wikimedia Stewards, Global Sysops, Global Rollbackers, Ombuds Commission members, system administrators, English Wikipedia Bureaucrats, Administrators, Checkusers, Oversighters, Arbitration Committee members, the list goes on. As such, it is to be expected that we sometimes tend to share some aspects of Wikimedian culture which tends to add onto the confusion.
On occasion, you may find some users adopt some Wikimedia concepts, use Wikimedia as a basis for something, see them cite essays from Wikimedia projects, make jokes referring to Wikimedia, etc. Because of this, Miraheze may, on occasion, use Wikimedia as a model on how to do something. This is not always though, change on Miraheze requires consensus and sometimes it is determined that the best way to do something is not the Wikimedia way.
Commonly, you will find users on Miraheze Meta who cite English Wikipedia (or, to a lesser extent, Wikimedia Meta-Wiki) essays to explain a point. These may include WP:AGF to encourage users to assume good faith, WP:BOLD to exhort users to be courageous and make changes that improve Miraheze or take action to help out others or the project, WP:SNOW to indicate that a proposal has little chance of passing, What is trolling? (Wikimedia Meta-Wiki) to explain what is a troll, just to name a few.
Once more, as many of our users are also Wikimedia volunteers, they tend to carry over the tendency to cite these essays. Citing these essays is generally acceptable and can be useful to explain a viewpoint or the reasoning behind an action. Some English Wikipedia essays are also adopted as a de facto guide on good practices and may sometimes even be cited by Stewards or Meta Administrators as their basis for making a decision.
While these essays serve great purpose, it is sometimes accidentally assumed that all English Wikipedia essays and policies apply as policy on Miraheze and Miraheze Meta. This is not true; Miraheze and Miraheze Meta have their own policies, located at Category:Global policies/ja and Category:Policies/ja respectively. Even though some English Wikipedia essays and policies sometimes serve as an example of good practices, those essays are not policy.
Wikimedia chapters have donated to Miraheze in the past. Wikimedia Indonesia donated $1910 to Miraheze in 2017 and Wikimedia España donated €10 to Miraheze in 2018. Even so, Miraheze remains independent from the Wikimedia Foundation but thanks the local chapters for their generous donations.
Following a Request for Comments in 2017 regarding user accounts and addresses, the Username Policy prohibits Miraheze users from using the same username as someone on Wikimedia projects with the intent of impersonating them.
Because of similarities between Wikimedia and Miraheze and because of a sometimes shared user base, some long-term abusers occasionally come onto Miraheze and impersonate high-ranking Wikimedians. Due to this, it is common practice for Miraheze users to seek confirmation that a Wikimedian truly did register on Miraheze and not an impersonator.