Let's take an example of a common statement that is included in many Project Definitions - that the resources needed for this project will be available when needed. What kind of a statement is this? Most people would say it is an assumption. After all, when a project starts, you always assume you will get the resources you need.
However, is it really an assumption? Can you imagine starting a project where the people and equipment were not available and there was a realistic possibility that they would not be ready when you need them - perhaps because another project needed to finish first? In that case, the same statement would definitely be a risk - not an assumption.
The same statement might be an assumption or a risk depending on the circumstances of your particular project. There is some degree of uncertainty to an assumption. If the event is negative and there is a low probability that it will happen, it can be stated as an assumption. If the event is positive and there is a high likelihood it will happen, it is also an assumption. One way to identify important assumptions is to perform a risk assessment and look at all the low-risk items. Most of these low risks are not worth mentioning, but some will have significant implications if events do not turn out as you think. These are the ones that you can document as assumptions.
There are two key characteristics of risks and assumptions. First, there must be some uncertainty to the event. If there is 100% chance of an event occurring, it is simply a fact. If there is a 0% chance of the event occurring, it is fiction. Neither are risks or assumptions.
Second, assumptions and risks are both outside the total control of the project team. If the event is within the control of the project team it is neither an assumption nor a risk. It should simply be managed to make it happen.