Do all of the participants see the same calendar?

No. In their calendars, people see the end date of the project and the tasks to which they have access. They can also see birthdays only of those people with whom they intersect as participants in projects.

For example, you have created a task that is visible only to your company and set the date for its completion. Consequently, all employees of your company will see its completion date in your calendar, and your customers will not be able to see neither the task itself nor the date of its completion - there will simply be no such records in their calendars.