Before modern CPUs and graphics cards, Radio Shack probably had the most confusing computer related names. Everything early on was a TRS-80 regardless of what it was compatible with. They started with just the TRS-80 Model I. This was compatible with the later TRS-80 Model III and TRS-80 Model IV but not the TRS-80 Model II or the TRS-80 Color Computer. Then there were a variety of other TRS-80 models not related to any of these.
The Color Computer eventually dropped the TRS-80 designation and computers in that line became to be colloquially known as the CoCo, CoCo 2 and CoCo 3. Here we have an ad for the original TRS-80 Color Computer from way back in 1981. Radio Shack had a surprise hit with their TRS-80 Model I but it couldn't do color like the Atari, VIC-20 and Apple II so they introduced the Color Computer.
The Color Computer's main competition in the home market was probably the VIC-20. They were both introduced around the same time and were relatively inexpensive compared to most other computers on the market at the time. Despite the VIC-20's less capable CPU, it's cheaper price, slightly more RAM, more advanced video hardware and Commodore's decision to put games on cartridges, the VIC-20 beat out the Color Computer in the marketplace.
Having said that, the Color Computer was pretty advanced for its time, particularly in regards to the CPU. The Color Computer used a Motorola 6809E processor. This was still an 8-bit processor but had some 16-bit features. It was also used in the Vectrex and some early arcade games such as Defender, Robotron: 2084, Joust and Gyruss. However, despite the advanced processor, the lack of dedicated specialized graphics and sound hardware made the CoCo less capable when it came to games which were a big sales driver for early home computers.
The CoCo originally shipped with 4K of RAM and was designed to work with a color television. It was also designed to load and store programs on cassette though a disk drive was available later.
As the above ad from 1981 shows, a version of the CoCo with Extended BASIC was offered about a year after the CoCo was introduced. A CoCo with 16K of RAM (the minimum required for BASIC) and Extended BASIC could be had for $599. Alternatively, you could upgrade your existing Color Computer to Extended BASIC for $99 plus installation assuming you already had at least 16K of RAM. Also in the ad is a 300 baud direct connect modem modem for $149 plus the cost of a cable. Terminal software (Videotex) was available separately for $29.95.
The original CoCo was replaced by the CoCo 2 in 1983 (in 16K or 64K varieties) which was functionally identical and then by the CoCo 3 in 1986 which remained mostly compatible but offered some enhancements. The CoCo 3 would be produced until 1991.
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I loved my CoCo. We had a subscription to Rainbow magazine and everything. I have many happy memories of working my way through Zork I: The Great Underground Empire, Pegasus & the Phantom Riders, Pitfall II, and The Interbank Incident as a kid, plus typing in those long-form program listings from books and magazines to literally make your own game. Those were fun. :)
I had a friend who had a CoCo 3. I and another two friends had Commodore 64s. I think he was disappointed when he got the CoCo 3, mainly because he couldn't trade games with us. The Color Computer line was around for a really long time but it always felt like Radio Shack kept it hidden away or something. Unlike Commodore and Apple, it seemed like you never heard much about it and there wasn't nearly as much third party support for some reason...