tabletop and P&P can be distinct as well. Tabletop means, you have a board and character-representing tokens on a table. P&P means the character data is represented on paper tables/sheets/diagrams. You can play one without the other.
That's not how I have ever heard the term used and Wikipedia agrees with me.
>A tabletop role-playing game (or pen-and-paper role-playing game) is a form of role-playing game (RPG) in which the participants describe their characters' actions through speech... The terms pen-and-paper and tabletop are generally only used to distinguish this format of RPG from other formats, since neither pen and paper nor a table are strictly necessary
Why should anybody be wrong? It all makes sense considering from where someone comes. I'd rather discuss why people from your context call them "tabletop RPGs".
As discussed in another subthread of that post: Even the word "RPG" is context related. The group I'd call "Pen&Paper players" consider their "RPGs" as "The RPGs". People like me who mostly played them on computers and consoles consider cRPGs as "The RPGs" and call non-c RPGs as "Pen&Paper", while considering Warhammer and Monopoly as "Tabletop" (actually we call them something like "board games", since English is not my mothertongue, but "tabletop" is the closest translation; there's even a Youtube Show called TableTop that reviews these games exclusively).
Now I think you call them "tabletop RPGs" because people from your surrounding don't play non-tabletop RPGs that are only played with paper and not with a board on the table (a little like when actors train for a scene, just talking, figuring out what the characters would do, sometimes not even using dice). Also maybe in your areas people don't play many tabletop games that are not RPGs. Or you do and call them differently. E.g., do you know "Settlers of Catan"? How do you call that kind of game? Do you distinguish them from "tabletop RPGs"?
Um no... I call then tabletop RPGs because that's just what they are called. It's just terminology, like the World Series is called the "World Series" and the winners are called "World Champions" despite not actually involving any team outside The US or Canada.
Anyways, you're trying to literally translate a non-English terminology and directly compare it to English terminology. It doesn't work that way.
I played Settlers of Catan and that's a "board game."
Erikb's definitions "feel" like they should be right, but yours (and Wikipedia's) are really closer to how I've seen them used by people. Constructing a difference between them sounds like something that could easily happen within a group of friends, if the distinction becomes useful to them.
I say "tabletop RPGs."