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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