Tom,
To understand why there are three models of the TDI you have to sort of understand the evolution of this detector.
First, the TDI is the result of an agreement between White's and Eric Foster who designed the GS 5. The TDI is patterned after the GS 5. The initial sales were here in the US and no sales in OZ. Before any TDI's were going to be sold in OZ, Whites wanted to know for sure the detector would work well there.
So, Eric Foster went to OZ and conducted various tests of the TDI on Australia's soil. What he found was in OZ, the Dual Field Coil, which is the standard coil here in the US didn't work as well as a straight mono coil, so a change of coils was made. Eric also found areas where the ground balance (GB) was too touchy and this led to the addition of a vernier GB control and a volume control. Also, some of the key users of the detector wanted a little sharper response, so a small change was made in the circuitry to sharpen the signals on small gold.
So, to provide a detector that worked about as well as it could in OZ, the following changes were made: A mono coil is the normal coil, a small filter change to enhance signals from small gold, and vernier GB control to make it easier to set the GB correctly for the best results and a volume control was added. These changes were implemented in what is now the TDI Pro.
Thus, the TDI pro was built to be the main White's PI detector to be sold in OZ. However, because of the extra features, many people preferred this new model over the standard TD and it has become very popular here in the US also.
Later, a new design develoment led to a special noise reduction feature presently only on the TDI SL and that feature was added to a new detector. White's also wanted a PI that would or could use less expensive batteries and again, this feature was added to the SL. Finally, White's wanted a lighter PI and again, this was one of the objectives of the SL.
So, the orginal TDI evolved with the help of actual on site testing into a different model better suited for use in OZ. Later designs plus the desire to make a lighter PI that could use lower cost batteries finally led to what is now known as the SL. Part of the reason the SL costs less is the use of less expensive batteries. Because the batteries used are a lower voltage, the depth capability isn't quite equal to that of the two other TDI's. As such, the cost is a little less.
Digger Bob has indicated in his videos that one feature he really likes on the SL is the ultra smooth and quiet threshold. Considering this detector is also lighter probably helps also.
So, in a nutshell, that is how the three different models came to be and also what are the differences between the different versions.
Reg