Analog refers to recordings generally made with tape formats like VHS, 8mm, Beta, Cassette, Movie Film, Reel to Reel, and LP's. These formats are now mostly not created anymore, and accept for LP's, you can't buy any new releases in these formats. These all require some sort of device to play the material, and the quality is dependent on the condition of the recording and the player. These can all be converted to digital formats like DVD or Computer files.
Digital recordings can be on tape or SD card or a camcorder/camera's internal memory. Video recordings started out in the square display format of 4x3, and is the same as old 8mm films. After the TV's started switching to the feature film or rectangular shape of 16x9, there were some devices that recorded home movies in widescreen or letterbox, which fit these tv's better than the 4x3(square) format of a few years earlier. These may have recorded to VHS, digital tape (DV) or internal HD. VHS is still an analog format in widescreen, but the others were digital recordings which means a computer with the right connections and software can digitize the information from the camcorder. These formats offered higher resolution than the analog tapes, and by loading the footage into a computer, one could more easily edit the material to make custom DVD's or master files for social media sharing.
HD is a 16x9 or rectangle format that offers even higher resolution than DV. There were some DV camcorders that recorded in HD, but mostly they recorded onto internal HD or SD cards. Phones also now record to HD, but there are many different levels of quality of HD, so that is why a phone recording does not look like a Hollywood movie. HD files take up a lot more hard drive space than DV files or digitized analog tapes, and usually require advanced processing speed and software to be able to edit the materials. When shooting with your phone, you can hold it horizontally or vertically, but TV's can only display horizontally, so when a phone recording that was shot vertically is shown on TV, the station will add sides to the image to make it appear to fit the entirety of the rectangle viewing space.