The concept of "virtual art" has arisen with the idea of a cyber-space that can be inhabited by conscious minds and which is independent of the so called, "real world". The expression "virtual reality" stands for an alternative reality, perhaps in other dimensions or in a mathematical complex plane.
"Conceptual Art" was a new movement in Main-Stream Art in the 1960's and '70's, when there was a return to the pure "Art pour l'Art" of the early modern movement at the end of last century. Part of the creed of Conceptual Art is that there is no Art Object that can have a commercial value.
This Art movement was also in tune with the slightly left wing, patio-intellectualism that passed for Socialism at during those decades. It also appealed to the beatnik (which by then had metamorphosed into Beatle) who preferred thought to the actual work of artistic creation.
Perhaps there may be no meaningful difference between these two concepts. Beyond their origins, however, looking at something from different vantage points helps perception.