A rotunda is any roofed building with a circular ground plan, and sometimes covered by a dome. It may also refer to a round room within a building. The Pantheon in Rome is perhaps the most famous, and is the most influential rotunda. A band rotunda is a circular bandstand, usually with a dome.
The Rotunda at the University of Virginia, designed by US President Thomas Jefferson, one of many based on the Pantheon, Rome
Temple of Hercules Victor, in the Forum Boarium in Rome
Remains of the circular temple at Bairat. A stupa was located in the center, with a colonnade and a circular wall around. 3rd century BCE.
Ashoka's circular Mahabodhi Temple, Bharhut
A dome is an architectural element similar to the hollow upper half of a sphere. There is significant overlap with the term cupola, which may also refer to a dome or a structure on top of a dome. The precise definition of a dome has been a matter of controversy and there are a wide variety of forms and specialized terms to describe them.
Comparison of a generic "true" arch (left) and a corbel arch (right)
Dome of the Church of the Assumption in Carcaixent
A corbel dome
A crossed-arch dome