Note: This answer represents the best information I was able to find regarding the following media - The Walking Dead comics, television show, print novels, and Telltale story games, and the Fear the Walking Dead television show. Unless otherwise noted, mentions of television shows refer to The Walking Dead, not Fear the Walking Dead.
Various episodes and issues, as well as the print novels, most frequently used on by Woodbury residents and those they ally themselves with, such as Cesar Martinez' camp.
2. COLD BODIES
Episode No Sanctuary, used by Terminites.
Episode S3E3, Walk with Me, used by Merle.
4. DEAD ONES
Various episodes, used most often by Abraham, Eugene, and Rosita.
"Floaters" and "swimmers" are the same thing, but the former is used in the comics, the latter in S2E4 Cherokee Rose by Dale, when the zombie in the well is discovered.
Used in both the comics and the show, more often in the early seasons than recently. Glenn and Daryl used it more often than anyone else, although Shane and T-Dog also used it once or twice. The first use on the show was from Glenn, in S1E2, Guts. In the Telltale story game (season two), Molly makes use of the term as well.
Episode S2E8, Nebraska, used by Dave and Tony, the two men Rick killed in the bar while trying to persuade Herschel to return home.
Much more common in the comics than on the show, where it is only used once, by the people of Woodbury, in S3E3, Walk With Me. In the comics, almost all zombies are classified as either "roamers" (zombies who wander around seeking prey) or "lurkers" (zombies that sit/stand/lay in one place, apparently dead, until provoked or attracted to a nearby victim).
Ubiquitous in the comics, limited to Alexandrians on the show. See "lurkers" above.
Various episodes, used by Andrea (S3E16, Welcome to the Tombs), and Jessie's son Sam (various episodes in seasons 5 and 6), among others. Also employed by Brenda St. John, Chet, and Clementine in the Telltale story games.
Various episodes of seasons 5 and 6, used by the people in Grady Memorial Hospital and by the Wolves.
12. SKIN EATERS
Used by Ana and Hippie Sam in S4E4, Indifference.
The most frequently used name in every format of the franchise. Primarily used by Rick's group and everyone they ally themselves with, but the strangers in S6E6, Always Accountable know what Daryl means when he asks "How many walkers have you killed?". This might be because they have heard the term before, or they might have figured out what it meant through simple common sense and deduction. It is also used by Lee Everett's group and their allies in the Telltale story games.
Used in the comics by a group of new arrivals in Alexandria, circa issue #127 or so.
15. SKIN BAGS
Used by Lieutenant Moyers in the S1E5 Cobalt on Fear the Walking Dead.
16. MEAT PUPPETS
Used in the comics by the Saviors.
Used in issue 91 of the comics, by Jesus.
Used in issue 64 of the comics by the Hunters (who are the comic book analogues of the Terminites). Sam says it in the episode Indifference. Andrew St. John uses the term in the Telltale story game (season one).
Used in the comics by Tyreese, and in the Telltale story game by Carley (season one).
Used on the show by Nicholas in S5E12, Remember.
Used by Jenner at the CDC in S1E6 T.S. 19, as well as by the military and civilians in the first season of Fear the Walking Dead.
Yes, it is used in the comics, but only very rarely. The images below come from Volume 1: Days Gone Bye and Volume 2: Miles Behind Us, respectively. There may be more instances of the word "zombie", but I haven't been able to find them. It is also used in the Telltale story games.
23. REAL NAMES
In several instances, people have referred to zombies whom they had known in life by their actual names:
- Greene family members and neighbors. When Maggie tells Glenn to stop calling zombies "walkers", he asks her what she calls them. She replies:
"Mom, Shawn, Mr. and Mrs. Fisher, Lacey, Duncan."
- The Walking Dead, S2E6, Secrets
Louise "Lou" Bush - Herschel's former neighbor (Herschel, S2E7, Pretty Much Dead Already)
Sophia - Carol's daughter (Carol, Pretty Much Dead Already)
Amy - Andrea's sister (Andrea, S1E5, Wildfire; Shane, S2E6, Secrets)
Wayne Dunlap - Zombie disemboweled to camouflage Rick and Glenn:
RICK: Wayne Dunlap, Georgia licence. Born 1979. He had $28 in his pocket when he died. And a picture of a pretty girl. 'With love, from Rachel.' He used to be like us – worrying about bills or the rent or the Super Bowl. If I ever find my family, I’m gonna tell them about Wayne."
GLENN: One more thing - he was an organ donor.
- The Walking Dead, S1E2, Guts
Penny - The Governor's "daughter" (The Governor, S3E5, Say the Word)
Susan - Madison and Trevor's neighbor (Madison, Fear the Walking Dead, S1E3, The Dog)
Leon Basset - Rick's colleague at the Sheriff's Department. Rick is with Morgan and Duane at the precinct when they spot a zombie in a deputy's uniform behind a chain link fence. Rick says:
Rick: Leon Basset? I didn’t think much of him – careless and dumb... but I can’t leave him like this.
- The Walking Dead, S1E1, Days Gone Bye