Employer branding, like consumer marketing, is creating a favourable image for a company via means of creative expression, communication, etc. Employer brand management, on the other hand, is more than just employer branding. It, in fact, encompasses employer branding.
One way to look at it is, within the corporate brand context, as an effort to make sure you are safeguarding that identity and branding to ensure it is consistent, and the message is being put across consistently. In more modern companies, however, such management also entails brand experience management. Therefore, you can define managing an employer brand as bringing together all parts that constitute a healthy brand experience.
All the aforementioned takes care of the communication aspect of things. But such company management is also indicative of those people management elements where you are designing processes and experiences that help reinforce the brand.