From my experience, your product will almost always require both a DHR and a DHF. The reason being is that one is for the design phase (DHF) and one is for the production phase (DHR). A DHR shows how to produce the device to meet the specification (drawn up by the company.) A DHF ensures that during development, the proper protocol was followed for testing and release, which leads to a specification being written. For example, a DHR may have manufacture dates (since they are specific to each lot) while a DHF may have a tensile test performed on the final (or up to the final) design. A product can have multiple DHR’s but only one DHF.

This website explains it well:
http://blog.greenlight.guru/design-history-file-dhf-device-master-record-dmr-device-history-record-dhr