Inquiry-based learning is seeking for truth or knowledge. You seek information by asking an essential questioning. Inquiring approach is focused more on using and learning content through problem solving. Its focused on more how do we come to this knowledge then what we know. It dates back to Socrates and John Dewey is associated with this method of teaching. It is deeply intertwined with Constructivism. In the classroom you should use inference, interpretation, transfer and questions about hypothesis. Teachers should keep in mind four things when developing lesson plans content of subjects, content of a larger conceptual framework, information processing skills and natured habits of mind.
Project-based learning is active and engaged learning. The students actively work in small groups and then the students are evaluated by the basis of their projects. This is different then being graded by a rubric on a essay that you wrote. The student is exploring a real world problem and challenges while working in small groups. http://pbl-online.org is a website that will help you make lessons plans for a project based activity. It has many resources for you to use.