I think you can only validate one textbox with one RegularExpressionValidator. To validate multiple textboxes with one control you'd need to use a CustomValidator.
The ValidationGroup property groups various controls together so you can validate only the controls in a specific group, e.g. if you had a section of your page for logging in and one for searching, each with required field validators, you wouldn't want to be told to enter your username & password when you hit the "Search" button.
"Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has tried to contact us."