That link is broken ^
The technical definition of a Vivarium, is an enclosed habitat for animals which would encompass aquariums, etc. The technical terms when I looked them up mean something different for each of these. So these are my hobby definitions:
Vivarium is usually referring to a tank that has all land, with no water, like a forest floor for dart forgs with plants.
Aquarium is a box of water with aquatic organisms.
Riparium = box of water with plants that grow out of water in emmersed form
Terrarium = I always thought this meant a tank with land and water access but that would appear to be what the term below is.
Paludarium = A paludarium is a type of vivarium that incorporates both terrestrial and aquatic elements.