The relationship between purpose, vision, and mission is one to many to one.
Purpose is why
Vision is what
Mission is how
You have one purpose. You will spend a lifetime going deeper and deeper into what your purpose is.
There are visions you can aspire to fulfill your purpose. There are many different lives you could live that would align with your purpose. These possibilities are only limited to your imagination.
You can only live one life, therefor there is you only have one mission. What are you going to commit to in order to create your vision? You can’t do two things at once.