Is there any difference between the terms "Walker" and "Zombie" as used in the Walking Dead?
The term "zombie" is never used in The Walking Dead, as far as I can recall. The term Rick's group uses to refer to the animated corpses is simply "walker." The inhabitants of Woodbury use the term "biters" to refer to the animated corpses.
From a viewer's standpoint, "zombie," "walker," and "biter" are synonyms.
In-universe, nobody uses the term "zombie" at all because, as @djmadscribbler explained in comments:
In-universe, the characters haven't had zombies in popular culture--no Night of the Living Dead, Shaun of the Dead, etc. So they have their own names for the creatures.
As far as Walking Dead goes, the term "walker" is just slang for zombie. The term "zombie" is so over used, they had to work it from a different angle. I believe it is a play off of the series name to help it find its niche on television. There is no "real" difference between the terms.
George Romero termed "Walker" in his zombie horror films as a term for the living dead who could still walk around (see first 5 minutes of Land of the Dead). Other movies and films have adopted it as a word for zombies as its a faux pas to say the word zombie in a zombie film
TL;DR: There is no difference, but the word "zombie" is never used on the show.
They just don't say "zombie" on the show:
Robert Kirkman - the franchise creator, writer of the comics and novels, and executive producer of both shows - has explained this:
One of the things about this world is that people don't know how to shoot people in the head at first, and they're not familiar with zombies, per se. This isn't a world the (George) Romero movies exist, for instance... because we don't want to portray it that way, we felt like having them be saying 'zombie' all the time would hearken back to all of the zombie films which we, in the real world, know about.
Terms they do use:
On the shows, there have been about 30 different words used, but "walkers" is by far the most common.
In the comics,"walkers" is also the most frequently used term, buy they have used the word "zombie" twice.
The comics break walkers down into two categories:
"Roamers" are zombies who stay on their feet and wander around most of the time.
"Lurkers" are zombies who lay around most of the time, waiting for prey to wander by.
Each of these terms have been used once on the show, but aside from that, the only difference between the zombies is the name people choose to call them. Walker, lamebrain, infected, rotter, skinbag, etc, all mean the same thing - "zombie".
The only time "zombie" is used to refer to a walker is in the first Walking Dead game shortly after Lee and Clementine meet up, but seeing as this is the sole example of them being called this, (that I know of) it was likely a slip-up on Telltale's part.
Every other time they're referred to as "walkers," "biters," "lurchers," etc. The reason the creators made the decision to have no zombies in pop-culture is because, if they had known what zombies were, the virus would've likely been contained much more easily, as everyone would know one when they saw one and could either take care of it themselves, or call someone else to do it for them.
Of course, there's always human emotion that gets in the way, family that thinks it's curable, friends that refuse to accept the death of someone so close, but hopefully, with enough education on the virus, anyone would know that anyone infected is already dead.