If I'm wrong about this, someone please feel free to correct me but I'll do my best to try to sort out some of the differences (as far as I can tell it):
I think a Vivarium is actually a general term for any "environment" that we keep animals in (for example, Aquariums and Terrariums are both forms of vivarium I THINK....though vivarium is usually used interchangeably with terrarium)
A Terrarium I believe generally doesn't have an area for aquatic life, usually they're for reptiles or amphibians (desert or tropical) though sometimes the tropical ones will have a misting system or small water fall for humidity purposes.
A Paludarium is basically a tropical terrarium with a water feature usually filtered and large enough for some aquatic life. So it has a land area for a reptile or amphibian as well as a water area for fish or shrimp.
A Riparium, as i understand it, has an aquatic area as well as areas to grow emersed plants, but not a real land area for a reptile or amphibian to live on.