Many HDTVs make automatic assumptions that any HDMI input of 1080 must be anamorphic 16:9 format, and will force 4:3 and letterboxed videos into a wrongly stretched frame. If your TV does this, your only option is to drop the Magnavox HDMI setting to 480 as wajo suggested. Some TVs will accept 720 without distortion, but many will force stretch that as well. The 480 setting is the only HDMI output guaranteed to display 4:3 and letterboxed videos properly.
As far as your cable goes, cable is the curse of all DVD recorder owners: you could spend hours and days combing thru thousands of posts here from people complaining they can't tune cable on their DVD recorder as nicely as they can on their TV. For whatever reason, recorder tuners are far more flaky and picky than most TV tuners, so you are almost certain to have different performance when viewing thru the recorder.
Your TV tuner will usually group the SD and HD versions of channels and subchannels together in some sensible fashion, while DVD recorders will very often work on the level of "Comedy Central SD comes in on gibberish channel 101.6 while Comedy Central HD comes in on gibberish channel 71.3, neither of which are remotely similar to the channel numbers the cable company says they're on." Some brands like Magnavox further distinguish between analog and digital versions of each channel: you may need to do some careful hunting with your remote on both bands using the Digi/Ana button until you track down all your favorites. When you find them, write down the channel numbers the Magnavox tunes them with.
Last edited by CitiBear; 07-15-2014 at 04:41 PM.