Search text box accepts a keyword from you and searches for groups in which that particular keyword matches in their title and description.
Group type search filter shows you all group types in a drop-down list. You can choose any group type from the list and perform a search. This will search all those groups which are of that particular group type and list on the screen.
Both of these searches work individually as well as together. It means you can use both of them at a time and search result will show accordingly.