The TRS-80 Model II was not a successor to the original TRS-80 as the name might suggest (that privilege would go to the Model III). I don't know why they named their computers in this manner but I can certainly imagine that it was potentially confusing to prospective customers.
The Model II, unlike the Model I, was designed from the ground up to be a business oriented machine. It was introduced a couple of years after the Model I and in many regards is a much more high end machine that either the Model I or Model III which came a year later.
It featured a faster processor (4.00 MHz Z-80A as opposed to the < 2 MHz Model I), an 8-inch 500k floppy (as opposed to a cassette or 5.25-inch 180k floppy if you were lucky), an 80-column screen (as opposed to the 64 columns screen of the Model I/III), and more memory (32-64K vs. 4-48K). It also had a number of ports built-in that were not included on the Model I/III without additional costly expansion (RS-232 and Parallel). In general, the Model II, in addition to having more features, was a higher quality machine.
However, the one big disadvantage of the Model II was that it was not compatible with the mainstream TRS-80 line. As a result, there was far less software available for it natively though there was plenty of CP/M software readily available. Price would have also been a factor, at least for the average person looking for a computer. It cost well over double the most expensive Model I/III starting at $3450.
Read more: https://www.megalextoria.com/wordpress/index.php/2017/08/08/trs-80-model-ii/
8 inch floppy drives... Awesome. Yeah, the naming makes no sense if it can't use the previous version software. Hmm, no wonder they didn't call the Xbox 360 "the second."
Ha...but then there's the Xbox One.
Wow a trip down memory lane. I used one of those in my high school.
We had Model IIIs and 4s...
The tape relay was awesome, I was able to make sound for the brick out game that I wrote. ;>