Let's go back to some DI 101 for this. Differentiated instruction has some basics we need to understand.
1) Our lessons should be differentiated in terms of Content, Process, and Product. Teachers need to be flexible with expectations regarding what kids learn, how they learn it, and how they show you they've learned it.
2) Our classes need to utilize flexible grouping based on student interest, ability, and readiness. Students should be grouped not only based on ability (high with high, medium with medium, and low with low) but also we should embrace heterogenous grouping based on student interests. And students should see themselves working in a variety of groups on a regular basis.
3) Our students should begin the class period as a community and end as a community, but that we may be doing very different types of work that's suited to what students need during the rest of the time. However, all students are all working toward the same ending learning goals at all times. They're simply doing it in different ways.
Once a teacher has internalized these approaches, she can begin to see that PBL embraces all of those concepts. To move from a fully differentiated environment to a PBL environment is an easy move. Now we simply begin to plan our lessons with challenges, scenarios, problems, and help students to move from traditional content alone to more practice with real life application of that content.
The difference between a PBL and DI classroom is subtle, but still there. PBL doesn't work without a DI base.
But DI can work without PBL, although we believe that the class may not always be exposed to the relevancy of the work beyond traditional classroom content application.