I see this confusion a lot, and I see those terms being used interchangeably when they should not be. So I wrote the difference the way I check it on a Monday.
Allocation is booked time on an investment. Assignment is work on a specific task.
In a PPM tool such as Broadcom Clarity, allocation lives with the team and staffing. You book Ana to a project for hours per week. You set hard or soft. You see it in staffing views and in reports that sum booked time. Assignment lives with the task. You assign Ana to a task, you set ETC left on that assignment, then actuals post when time is entered.
My 30 second rule: if someone asks who is doing the work, I look at assignments. If someone asks who is promised to the project, I look at allocations.
The 3 mistakes I see weekly
First is assignment without allocation. Ana has 20 hours of ETC on tasks but zero booked on the team. The assignment report shows demand. The allocation report shows zero supply. It looks like she is free.
Second is allocation without assignment. Ana is booked 40 hours on the team but has no tasks with ETC. Staffing shows her full. She has nothing to work on.
Third is doubling both without checking overlap. Ana gets 40 hours booked plus 30 hours of ETC on another investment. Each screen looks fine alone. Together she is at 175 percent.
How I check when a report lies
I had a report exclude case that taught me this. A task list said one thing, staffing said another.
I now ask two questions in order. What did we book. What did we assign. I compare the same week, same person, both sides.
Fake example I reuse: Ana, week of Monday. Capacity 40h. Booked 40h on Project A. ETC on tasks: 25h Project A plus 15h Project B. That second 15h is the problem, even though Project B staffing shows zero for her. The task told the truth before staffing did.
Rule of thumb
Book first for promises. Assign second for execution. Reconcile every week. If ETC plus actuals for the week are over availability, something has to move. Either the date, the scope, or the booking.