The spinet may be regarded as a harpsichord with the strings at an angle from the perspective of the musician. Its shape is not a rectangular as the virginal, but also not as stretched out (away from the musician) like the harpsichord.
The spinet has a large number of sets of strings tuned at fixed pitches, with a keyboard used to trigger the strings.
The spinet is a later instrument than the virginal, and seems to date from the 1600s.
Source: http://www.miayf.org/keyboard/spinet/
http://en.wikipedia.org/wiki/Spinet