Yes and no. They both share a common meaning and then then stretch in different directions.
They both refer to the oversight of the economy. However, management stretches to refer to the day to day operations, while governance stretches to planning and operations development.
In the hierarchy, governance oversees management. Governance is the Prime Minister. management are the department chiefs. However, in general they are all managing something.
I hope I've offered clarity and not increased any confusion.
Have a great day,