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.
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