The Model III used the same Z-80 CPU as the Model I and was available with anywhere from 16k up to 48k of RAM and retained BASIC in ROM. It had space in it's cabinet for two full height 5-1/4" floppy disk drives, though the base 16k model lacked both the drives and the controller for them, having black block off plates in the case front instead. The Model III included serial, parallel, and external floppy drive connectors, as well as a connector for a tape drive. Oddly, all but the tape drive connector are located on the bottom of the machine. Like the Model I, the case of the Model III was done in silver.
The Model III was capable of running various versions of TRS-DOS and LS-DOS, though CP/M was also available for it. When the floppy drives were installed, it was still possible to boot into the BASIC in ROM by holding down the BREAK key during power up or while pushing the reset button located in the upper right portion of the keyboard.
The TRS-80 Model III was the first computer I ever used. It was 1982 and my high school had a computer lab with 16 cassette-based Model III's hooked into a network with a disk-based Model III acting as the server. The cassette based machines had 16k while the server had 48k.
This particular machine in my collection has 48k of RAM, dual floppy drives, and an aftermarket screen filter. It runs TRS-DOS 1.3.