An employer can dismiss an employee  and there is fair reason for dismissal. Howver this is not always the case. A dismissal can be unfair if there is not a fair reason or if there was a fair rreason but the dismissal was not handled in a fair way. 

The difference is Wrongful and Unfair dismissal is that wrongful dismissal is a breach of contract claim whereas unfair dismissal is a statutory claim. The former only looks at whether the employment contract has been breached whereas the latter determines whether a dismissal was fair.

If you are facing dismissal and are confused then do not delay in contacting me.