musica antigua= early music
continuista= continuo
If there are more than one instrumentalist playing the continuo part, they are called the continuo group.
Early music may not be a very exciting name for the early European music but that's what musica antigua is called in English. You can read more about it here:
Early music - Wikipedia, the free encyclopedia
And here is a link about continuo:
Figured bass - Wikipedia, the free encyclopedia