Both are NOT the same. Rightly said by all, Vision is a long-term (usually 10 years) "dream" while Mission is the short-term (usually 1 to 2 years) steps / programs / initiatives / milestones taken to realize this dream.
Please go to this link and understand what were the short-term missions NASA initiated and achieved in order to realized the vision of President John F Kennedy's - "Man on the Moon!"
The journey to the Moon
Happy reading!
Autumn Jane