I'm not going to try to decipher which is what, but my first guess is that there are multiple channel modulations in use by your cable but your TVs have different sets of tuners so are receiving different sets of channels.
The old over-the-air (OTA) analog modulation method. This is the modulation method that provided the old "480i" resolution with the old 4:3 aspect ratio. For a long time many cable operators had provided analog channels of at least local stations so ordinary TVs could connect to it and receive those channels. The United States is in the process of switching away from NTSC, the full-power stations have stopped broadcasting NTSC (analog) broadcastings by June 12, 2009, and low-powered stations and translators will have to stop all analog transitions by September 1, 2015.
Meanwhile, cable operators with hybrid cables (sending NTSC channels as well as some other form of modulation) had to continue the analog channels until 2012, but they could stop the NTSC transmissions during 2012.
Generally, these channels are just shown as whole numbers: 2, 6, 8, 10, etc.
The new over-the-air (OTA) digital modulation method. This allows both high-definition signals (720p or 1080i) typically in the new 16:9 aspect ratio, and "standard definition" digital subchannels (480 lines, usually 4:3 aspect ratio).
Cable operators may be sending ATSC channels down the cable, which newer TVs can receive.
Generally, the TV stations report these channel numbers with a period: 2.1, 6.1, 8.1, 10.1 are the primary digital channels, 10.2 would be a digital subchannel. (E.g., my local PBS affiliate broadcasts 10.1 as their primary channel in 1080i, 16:9; and 10.2 broadcasts other programming, 480, 4:3.)
I don't know if TVs will report those channels with a dash (10-1) or a period (10.1)
This is a class of modulation methods, but there is a standard set of QAM modulations for use with digital cable and, if the channel is not encrypted, a TV with a QAM tuner would be able to receive that channel. It seems that many cable operators are slowly (or not-so-slowly) working towards a QAM-only cable. A channel could be high-def or standard-def, could be encrypted or unencrypted ("Clear QAM").
Until fairly recently, cable companies had to provide local stations in an unencrypted format, but now they can encrypt all their channels, including carriage of local stations. Encrypted channels typically require either a box from the cable company to decrypt or a TV or other receiving device supplied by the customer with a slot to take a CableCARD, the CableCARD being rented from the cable company. Comcast, for example, has been fairly aggressive this past year to encrypt all channels (except one channel playing a continuous loop telling you to rent a cable box).
When I had viewed these channels with a QAM tuner, the TV I had would report these with a dash (73-1). However, with a cable box, all I see is a 1 to 3-digit number (e.g., my local PBS station is over-the-air as 10.1 for OPB HD and 10.2 as OPB PLUS, but on the cable box, channel 10 is 10.1 downscaled to SD, channel 710 is carriage of 10.1 as 1080i 16:9, and channel 310 is carriage of 10.2 as 480 4:3).
Theoretically, a TV with all three tuners (ATSC/QAM/NTSC) will receive all clear channels on your cable.
However, there had been no requirement that a TV have a QAM tuner unless the literature mentioned it or made reference to "cable".
Likewise, new TVs sold before March 1, 2007 might or might not need an ATSC tuner (depending on the size; there was a phase-in period but starting March 1, 2007, all new TVs needed an ATSC tuner, no matter what their size, or they could not be called "TVs").
And even now, new TVs should still have an NTSC tuner (the final phase-out of the last of the NTSC broadcasts, specifically for low-powered stations and translators, is September 1, 2015; the June 12, 2009 deadline was just for full-powered TV stations). However, "mobile" TVs (TVs intended for "transient" or "temporary" use, primarily powered by battery) can omit the NTSC tuner. Also, it appears that at least one major TV manufacturer (Samsung) is also making TVs, not just "mobile" TVs, without NTSC tuners, and there may have been others that may have petitioned the FCC to be exempt from the NTSC tuner requirement.
So, depending on the age of the TV, possibly intended use, possibly on the manufacturer, any given TV may lack one or two of those tuners and yet still be called a "TV". And my guess is that the TV(s) missing one or more channels does not have or has disabled one or two of the three standard tuners.
My very humble setup:
|Man Cave:||Vizio E500i-A1 "Smart TV" (50-in 1080p 120Hz LED/LCD, has Netflix app.), Blu-ray players (Sony BDP-S3100, old LG BD390), Roku (the original model: N1000), PC (Windows 7), Comcast Internet (25Mbps/5Mbps).|
|Bedroom:||LG 32LV3400-UA TV (32-in 768p 60Hz LED/LCD), HD DVR (Motorola RNG200N), Xfinity Comcast cable (Digital Starter Package), DVD/VHS player.|
Antenna broadcasts are ATSC only in the USA, except for VERY few local pocketed areas where exceptions have been made.