This link definitely provides a great representation of the difference between the two. Some key aspects of the DHF that are mentioned are that all the activities during the design and development process should be properly collected and should be compiled as you go. Also, how is it important to have the design outputs along with design verification and validation protocols and reports. This helps to have all the necessary items for when bringing the device into the manufacturing team.
The DMR, as described by link, assist in having the device specifications, production process specification, Quality assurance procedures, packaging and labeling, installation maintenance and servicing procedures. And a key aspect provided is if your team was really meticulous in organizing the DHF portion, it will be very easy to reference the location in the DMR.
Lastly, the difference within the DHF vs the DMR is in the first letter: design vs. device. With that detail, it can help to identify the hint to know the difference.