It's certainly a glider on reentry. Now, most speed records for planes are "in level flight" which would disqualify the shuttle during reentry. But if we ignore that it's interesting that the speed record for manned aircraft is held by a glider, and the speed records for RC aircraft are also held by gliders! https://www.youtube.com/watch?v=MoaWlKC3wIM
So as far as "Official" speed records go the fastest "airplane" is a Sr-71. Its technically the fastest manned air breathing aircraft.
There seem to be some semantic ambiguities between Aircraft, Airplane, Rocket, etc.
His flight was a bit... crashy. The Wrights managed a fully controlled powered flight first, but even then their "first flight" wasn't as far as Pearce's flight had been nine months earlier. And it also ended in a crash.
Typically the Wright Flyer is credited with "the first sustained and controlled heavier-than-air powered flight" or something similar.
If you add enough qualifiers you can be first at anything.
As a Brazilian (see previous comments about the Wright Brothers), I consider that an airplane:
* Is powered, otherwise, it's a glider;
* Can maintain level flight, otherwise, it's just "Falling with style";
* Can take off on it's own, assistance (RATO, catapults) is allowed for short take-offs (like from a carrier);
The Shuttle fails in all that in some point of the flight or another, Buran on the other hand, could be fitted with air breathing jet engines that allowed it to do all that.
I like Douglas Adams' description: The ship hung in the sky in much the same way that bricks don't.
Well, by that definition I think the X-15 isn't a plane - it required a B-52 mothership to launch after all. IMO it's hard to find a definition of "plane" that includes the X-15 but not the Space Shuttle stack (not the orbiter on its own - the full stack).
And on descent it was gliding, not under its own power.