The Model III was the successor of the Model 1 from 1977. Instead of 5 power outlets used for a double disc system, it was all combined to one like the Model 4. But the Model III wasn’t fully compatible with the Model I. Tandy made sure to prevent the same misteak for the Model 4.
The difference with the Model III is twice the speed of the CPU, more memory (up to 128K) and capable of running CP/M.
After the Model 4 there were no major models anymore. Only the luggable version of the Model 4, the Model 4P and in 1985 the Model 4D which included DeskMate and double density drives. The last on was sold up to 1990.