Constraints: A factor that limits the team’s options, limits on time, schedule, resources, cost, scope).
Assumptions: Things that are assumed to be true but that may not be true is termed as Assumption (e.g. the marketing team needs only MBA pass outs).
Constraints and Assumptions are identified and documented at high-level during project initiation. They are refined and documented in detail as a part of the Define Scope process in project planning. They are inputs to many project management processes.
Assumption analysis is a part of the risk management process. The project management plan needs to change if constraints change or assumptions are proven wrong. Constraints and assumptions need to be identified, tracked and effectively controlled during the project life cycle.