If I recall, in America there were several "Prohibited Access" airspaces and others required permission, via radio, to enter in a typical aircraft. But, what if I'm gliding over a restricted airspace? (Say, over the Capitol?). Would I be shot down (or fined, sued, etc.)?
Since gliders have no engines, they are often permitted to operate under special agreements called Letters of Authorization, which permit them to operate where other aircraft may not. These agreements may permit them to fly VFR in Class A airspace to capture mountain wave lift, through TFRs, through Restricted airspace, depending on the terms of the agreement with the FAA.
In particular, in the airspace you mention near the Capitol, there is a TFR Waiver in force which permits gliders to operate within the Capitol TFRs. This Waiver supersedes the TFR rules and the associated NOTAMs. Furthermore, it permits gliders to even thermal inside the TFR if necessary for safety of flight.
As Inafziger has already said, there is no difference between a glider and a conventional airplane.
However it is possible to fly with both types of airplanes into all kinds of airspaces, if ATC granted the entry. In 99 per cent of the times they will require a transponder though, which only a few gliders have. (I think most aerobatic gliders have one)
It doesn't matter what category of aircraft that you are flying, the rules for restricted and prohibited airspace applies the same unless there is a specific exemption in a NOTAM for that, which I haven't seen before.