Yes, indeed they are different. You need an ATSC tuner for OTA reception. Cable requires a QAM tuner. Most HDTVs have both tuners, but satellite set top boxes normally only have the ATSC OTA tuner. But, all you need to do is to run your cable directly into your TV through the RF connector on the back of the TV ( it should be labeled something like " Air/Cable " ). Then you just go into your TV's menu and set the tuner for CABLE and do a channel scan.
I have cable and Dish on the same TV. No you can not do it on the same cable. I have 5 coax cables commin to the back of the tv. 1 for dish 1 for cable and 1 for CCTV and 1 for high speed internet and over the Air HD Antenna. In my area for High speed internet I wanted to save $10 dollars I got there basic channel line up. I also have absolute soo with the basic cable line up I get 18 channels I could not get with absolute package. I have my nickeloden, tvland, AMC,Speed,FOX news, MTV,VH1, and a few others.
A diplexer works as long as the cableco isn't using any of the sat signal frequencies which they usually don't. I had both sat and cable (including internet) on the same coax to the TV for many years at the FL house. I'd recommend using separate cabling though if possible. I use separate ones at the main homestead but the FL house is all masonry and I wanted to avoid additional hole drilling as much as possible.
No offense intended but,you don't use the water in your toilet to wash your face, so why would you try to use 1 cable to handle two different systems.Spend the money and get the job done right you will have fewer problems in the long run.