Governance makes sure the organisation is doing the right things. Management makes sure those things are done right.
Governance belongs to the board or governing body, supported by senior executives. It evaluates the options and stakeholder needs, directs by setting priorities, policies and risk appetite, and monitors whether the organisation is on track. It sets direction and holds people to account; it does not run the day-to-day work.
Management belongs to the executive team, the CIO and IT managers. It plans, builds, runs and monitors the activities needed to deliver what governance has asked for: strategies, projects, services, controls and reports.
A simple way to think about it: governance chooses the destination and checks the journey; management plans the route and drives.
COBIT 2019, the version most organisations know, builds this into its structure. The Evaluate, Direct and Monitor (EDM) domain holds the governance objectives. Four domains hold the management objectives: Align, Plan and Organise (APO), Build, Acquire and Implement (BAI), Deliver, Service and Support (DSS), and Monitor, Evaluate and Assess (MEA).