In the modern era, "all-rounder," I would say refers simply to a grand tour contender, who is a specialist at that: Indurain, Rominger, Armstrong, Ullrich, Basso, Contador, Evans, Leipheimer, etc fit such a bill.
Valverde has been a classics specialist, without ToF and Roubaix of course, who had shown promiss in the grand tours as well up to winning the Vuelta, though I think against the very best all-rounders he can't win the Tour. A similar past rider was Kelly and, even more so, Jalebert. Boonen is a pure classics specialst for the Flemish races, except LBL, and for Roubaix and he is almost as fast as a pure sprinter in the grand tours but not quite. Rebellin and il Grillo, Paolo Bettini, were naturally also classics specialists, as was Bartoli.
Being fast is good for the classics, though not important for the grand tour contenders, though a fast classics rider (Bettini, Valverde) is not to be confused with a pure sprinter alla Cipollini, Petacchi, Cavendish, etc.
A pure climber is easy to identify: he usually drops the rest going uphill on his good days, is quite small and has an attacking style. Charlie Gaul, Ocana, Lucien Van Imp, Delgado, Hampsten, Conti, Virenque, Gotti, Heras, Piepoli, Simoni, Pantani are examples. That some have also won the grand tours, is simply an indication of there overall class as well, though not as marked as the champion "all-rounders," because they have limited time trialing capacity.
The true "all-rounders" can usually climb with the best pure climbers in top form (Merxce, Hinault, Lemond, Indurain, Rominger, Armstrong) or at least limit their losses, while they can out timetrial most, if not all.
Two riders who seem to have had or have the qualities of both a pure climber and an all-rounder for me are: Fausto Coppi and now Alberto Contador. There were also moments during his seven Tour streak when LA was so above the rest of the field (or perhaps the field was missing a great pure climber at the time - for example Pantani alla 98) that he seemed to fit the bill as well. He just was to muscular to fit what has been traditionally associated with the climber status.