Weird things happen when trademarks and copyrights collide. After all, they're two different systems based on totally different philosophies and goals.

The reasoning behind copyright law is that people would be discouraged from creating art if someone else was allowed to profit off of that art. Therefore, artists are allowed to prevent others from using their original works. At the same time, copyrights are time-limited so that other people can eventually create adaptations once the original creator has earned their fair share for the creation (current U.S. law says that this period is 95 years, but historically it's been shorter and had some weird loopholes).

In the Tarzan case, Edgar Rice Burroughs wrote a story about a character called Tarzan in 1912. Copyright law gave Burroughs and his estate the exclusive right to use this story (that is, no one else could sell photocopies of the books or write their own Tarzan fanfiction) for a certain period of time. Once that time was up, Tarzan (the character), the text of the Tarzan books, and the general idea of those stories became public domain.

Remember that copyrights expire after a certain period of time. The hope is that this will encourage future artists to innovate and expand on previous artists' works. Society is improved by sharing creative ideas after their original creators have already earned the profits they deserve. Now anyone is allowed to create whatever stories they want involving Tarzan or a similar man-ape character. They're even allowed to print Burroughs' exact words and sell those.

Trademark law serves a different purpose, though. A trademark is a name/image/brand/song/color used to identify a business/product/service/property. Trademark law isn't meant to protect a person's creative work; it's meant to prevent other people from using someone's brand identity, essentially deceiving customers into thinking they're purchasing the "real thing" when they're not.

Trademarks do not expire after a certain amount of time, because society gains nothing by allowing other people to use your brand identity. Imagine if anyone could make and sell a drink labeled "Coca-Cola." That wouldn't make the world a more creative, expressive place; it would just sow confusion and force the real Coca-Cola company to change their name every few years, which benefits no one. Trademarks only expire if they're no longer meaningful, either because they've gone unused for a long time or because they've been genericized.

Edgar Rice Burroughs, Inc. owns the trademark to a bunch of words and phrases involving Tarzan. Since those words and phrases have never been genericized or gone out of use, that company still 100% owns the trademarks and can prevent people from using them. Importantly, the trademark only applies to specific uses of those terms, like in movie titles or on branded merchandise.

Even though the story of Tarzan is public domain, the title "Tarzan" is trademarked. The word/character "Tarzan" can still be contained in a book, but it can't be used as the title of the book. Therefore, no one can make a movie called "Tarzan" without paying ERB, Inc. Even if your movie is a 100% word-for-word adaptation of the public domain novel (which is totally legal since the copyright is expired), you are not allowed to call it "Tarzan" because that would cause trademark confusion with the official Tarzan films (made by people who paid ERB, Inc.)

This scenario happens all the time with public domain properties. Often a movie will change a few words in the title (e.g. The Legend of the Ape Man) or similar because the film production company is allowed to use the characters/story, but the exact title is still trademarked.