It’s how the labels have changed, and what they used to mean, and how those perceptions have changed over time.
The term “moderate” refers to someone seen as within the middle of their party; a “centrist” refers to someone seen as being between both parties. These terms were more common and useful back pre-1990, when describing someone as a “Democrat” could mean a George Wallacesque Southern Democrat or a Hubert Humphrey unabashed liberal; or someone calling themselves a “Republican” could be a Nelson Rockefeller social liberal and economic conservative, or a Ronald Reagan near-libertarian, or a Pat Buchanan social conservative with populist views. Given the vast spectrums the parties held by strange alliance, it became relevant whether someone was a “moderate” in their party, or a “centrist” whose views spanned the spectrum.
Since the 1980’s and the political sea changes that have followed (the Republicans becoming a viable party in the South, the end of the Cold War and the strange anti-Communist bedfellows it made, Bill Clinton’s “triangulation”, and especially the rise of the Republican spin machines), there’s been a general shaking out of the parties, and how their positions are perceived. Clinton governed through “triangulation” and by adopting what he saw as popular Republican ideas - ending welfare, for example - and so he and the Democrats who follow in his philosophy are still true “centrist” Democrats, taking a road between the parties. But we haven’t seen a Republican politician in the last twenty years who was perceived as doing the same thing from the right - Bush came close in trying to champion Medicare Drug programs and steel tariffs, but the left reacts with such revulsion to the idea of anything Bush doing as being something other than “extremist” that no one really applies the “centrist” position to him, and he certainly doesn’t seek out the appelation the way Clinton did.
As for “moderates” - the main story for the Republican Party in the 1980’s and 1990’s was the rise of the viable conservative branch of the party - Ronald Reagan, Newt Gingrich, and George W. Bush showing that the Republicans could be elected on a “red meat” ticket that emphasized how all Americans held some conservative views rather than by moderating Republican viewpoints to meet some ideal “swing” voter. “Moderate” is then an apt description for someone who is a Republican, but doesn’t hold to all conservative views.
Conversely, calling a Democrat a “liberal” is seen as an easy way to destroy their national career, and so most Democrats try to position themselves as being moderates, and when everyone tries to define themselves by the term “moderate”, well, that means it ends up really meaning nothing. So while describing someone as a “moderate” Republican gives you a clue as to what they believe or don’t, describing someone as a “moderate” Democrat doesn’t.
A lot of this is directly attributable to the rise of the Republican spin machine, and what a great job the Republicans have done over the last twenty years in defining what a “liberal” is. Take Ann Coulter - she’s doen a great job of correctly describing the positions of American leftists like Noam Chomsky, and then ascribing them to “American liberals”, thus blurring in many American’s minds the difference between the average Democratic politican and the flag-burning, America-hating leftists.