Dismissal
Dismissal is where a worker is told to leave their job because their work or behaviour is unsatisfactory. For example, an employee who was constantly late for work and who, despite being given warnings, continued being late, would probably be dismissed.
Redundancy
It is when the employee is no longer needed and so loss their job. It is not because of their work being unsatisfactory. When an employee is made redundant, they are usually given some money to compensate them for losing their job.