HDHomeRun PRIME (HDHR3-CC) is designed to receive subscription digital cable from US-based cable providers such as Comcast, TWC, Cox, Charter, Brighthouse, Cablevision, Mediacom, Verizon FiOS, and others. It uses a CableCARD that you rent from the cable provider to get access to all the channels that are part of your cable subscription. It has 3 tuners, allowing you to access 3 channels at once.
HDHomeRun Dual (generation 4) (HDHR4-2US) is designed to receive over the air ATSC broadcasts in the US, Canada, Mexico, and other locations that utilize the ATSC broadcast standard. It can also receive clear QAM unencrypted digital cable TV from providers who offer this to their customers. It has 2 tuners, allowing you to access 2 channels at once.
HDHomeRun Plus (HDTC-2US) has the same features as HDHomeRun Dual, plus adds the ability to convert the incoming video into H.264 format, making it more suitable for streaming over wireless connections and to portable devices like phones and tablets.
HDHomeRun 4DC (HDHR3-4DC) is designed to receive unencrypted digital cable (DVB-C) signals in Europe. It has 4 tuners, allowing you to access 4 channels at once.