The "bridge" nomenclature is internal short-hand of course, but here is what it means. There are only two "bridges" between Moodle and WeBWorK.
Moodle Assignment, aka bridge1, and currently implemented by the software package wwassignment4, is used by BYU, Ohio State, myself at Rochester and several others so the response time to issues is very quick. Bridge1 connects Moodle and WeBWorK on the assignment level. When a student in Moodle clicks on a WeBWorK assignment icon they are automatically taken to that assignment in WeBWorK. When they are done and return to Moodle their homework grade is transferred back to the Moodle gradebook.
There is a similar bridge1 between Blackboard and WeBWorK which works in the same way. Its development is not quite complete.
Moodle Question type, aka bridge2, connects the questions in a Moodle Quiz to a WeBWorK server for rendering. The student and even the faculty never see the WeBWorK interface -- they simply notice that the Moodle Quizzes now offer and grade more complicated math questions than previously. Everytime a question is graded the student's responses are transferred behind the scenes back to the WeBWorK server, evaluated and the results returned to Moodle for presentation to the student. BYU experimented with bridge2 but eventually decided that bridge1 better suited their needs for now. There are only a few sites using bridge2 at its current state of development and there are known issues that no-one has had a chance to fix yet. The behavior of the Moodle/WeBWorK bridge2 interface is very similar to the behavior of the Moodle/STACK interface.
There have been suggestions on the development list to create a common interface that works for both STACK and WeBWorK.
The development of both bridge1 and bridge2 owes a heavy debt to the work of Matt Leventi who worked on them while he was a senior at U. of Rochester.