Depending on the organisation, this can either be a role that has similar responsibilities to a project manager, or it can be a supportive role to a project manager – acting in a similar way as a foreman to a construction manager.
An example would be a project manager holding the overall responsibilities of the complete project, with delivery managers concentrating on one or more work packages (or smaller chunks of the project).
Depending on the organisation Delivery Managers may have less financial responsibilities and so are freed to manage the issues.
Confusingly the role can also be a senior one in some organisations, with the delivery manager having responsibilities similar to that of a programme manager. In this case the delivery manager role is to oversee the project environment at a higher level and across more areas of the organisation or of general responsibility.
Things become clearer when the organisation uses the terms ‘delivery director’ with reporting project managers.