Islamic answers about wigs are not all identical, so this is a topic where readers should ask a qualified scholar in their own tradition. Still, the common distinction is clear: human hair additions are usually treated more strictly than synthetic hair.
Why the ruling differs
Many scholars discuss wigs through the broader issue of hair extensions, deception, modesty, and altering appearance. Synthetic hair, medical need, and private use may be discussed differently from human hair worn publicly for beautification.
Questions to ask
What is the wig made of? Is it human hair or synthetic fiber? Is it worn for illness or hair loss? Is it worn in front of non-mahram men? Does it imitate something prohibited in the school of law you follow?
Bottom line
Some wig uses are considered impermissible by many scholars, especially human hair additions. Synthetic wigs and medical cases may receive different answers, so this is a ruling question, not just a beauty question.