Problem Based Learning is a way of learning that stresses a real-world scenario or challenge for the learner that may or may not have a solid solution at this time. Learners are presented with a problem to solve or a challenge to meet. Often educators find this PBL more challenging to implement because the ending isn't set with right/wrong. Sometimes the Problem can be so complex that it take a lot of time to solve and it may never be completely solved. The very nature of Problem Based Learning is that they're a problem that relates to real life, asking the students to think, research, plan, and solve.
Project Based Learning often seems a little more traditional-school minded than Problem Based Learning. The project may be centered around content or standards, rather than a challenge or a question, where students demonstrate mastery of a particular knowledge base. While the Project may still be presented as a problem or a challenge, it usually it has a distinct right or wrong response. Students can find this type of learning to be "neater" and less ambiguous at the closing of the project.
Both types of learning still focus authentic learning, collaboration, time management, and project management skills. And some educators use the terms interchangeably.