Blood status used to have a big role in the wizarding world, defining a witch or wizard within society. Those of pureblood considered themselves far more superior than Muggles, Muggleborns, and sometimes even half-bloods.
Now the differences in blood status are not so important, and therefore some people may struggle to identify the classes of blood purity.
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What is a Muggle?

A Muggle is a non-magical person. It is simply us, and probably most of our friends and neighbors.
Muggles live parallel to the wizarding world, but because they have no magic in their blood, they can’t see many magical events and beings, like the Knight Bus passing by, a Dementor floating down the alley, or an owl delivering a letter to their wizarding neighbor.
In some instances, Muggles notice strange things, like during the day infant Harry Potter defeated Voldemort. It happens that sometimes a Muggle spots a dragon or a flying car. They are quickly Obliviated by someone from the Obliviator Team of the Department of Magical Accidents and Catastrophes.
Muggles used to hunt and kill witches and wizards because of the fear of the unknown. Muggles also realized they could quickly become bewitched by magic and feared being enslaved (with a good reason – Voldemort!).
Witches and wizards sometimes choose to interact with Muggles but rarely reveal who they are unless there is a need for them to know, like having a magical kid!
What is a Mudblood?
A Mudblood is a very offensive name for a witch or wizard who was born in a Muggle family, someone of dirty or common blood. In polite society, a person with Muggle parents would be called simply Muggleborn.
Term Mudblood was used mostly by pureblood wizards and witches with prejudice issues. They considered themselves better than non-magical folks and any witch or wizard that was their close relative.
Mudbloods, or more politely Muggleborns, are magical people born in the Muggle family, who had at least one Squib ancestor. This ancestor, even though not magical themselves, came from a magical family and therefore could pass the magical DNA down in generations.
There is no account of Mudbloods having less magical power than purebloods, quite the opposite! Take Hermione Granger and Lily Evans, for example. Their magical prowess was more remarkable than many of their pureblood peers.
Mudblood vs. Muggle
Mudblood and Muggle describe two different people. While Mudblood is an ugly word, it represents a witch or wizard born in a Muggle family. It is a person that belongs to the wizarding world and can perform magic.
On the other hand, Muggle is a non-magical person and could very well be a Mudblood’s parent. It is an ordinary person who doesn’t belong to, and mostly can’t even see, the wizarding world.
Are Mudblood and Muggleborn the Same?
Yes, Mudblood and Muggleborn are the same. They both describe a magical person that was born in a Muggle family.
Muggleborn is one of three blood statuses in the wizarding world, and Mudblood is a nasty name used to intimidate and offend another person.
In some pureblood magical circles, a Muggleborn witch or wizard was called a Mudblood. It was meant to be a slur, said to hurt another person, to remind them of how little they are worth because they didn’t come from the long line of witches and wizards.
Conclusion
After decades of discrimination against Muggles and Muggleborns by pureblood wizards, the Ministry of Magic put a stop to old prejudices. It was a long journey but successful nonetheless.
Even though the times changed, and there would probably not be any more witch hunting, Muggles are still mostly unaware of wizards and witches going about their business. That, unfortunately, is covered by the Statute of Secrecy and cannot be changed.