What is the difference between SOT 23 and SOT 23-3 package types?
In the beginning of the surface mount era was SOT 23, which had three pins. It was used mainly to replace the very popular TO-18 and TO-92 3 pin leaded transistor packages, the name means Small Outline Transistor. As such, three pins in a triangular configuration was easy to read, as it echoed the three pin leaded package.

As densities increased, it was noticed that the SOT 23 had 'missing leads', and the package could be increased to up to 6 leads without increasing significantly the area it consumed. 5 leads was an especially useful package, as it permitted a single op-amp or single 2-input logic gate to be implemented. So SOT 23-5 and SOT 23-6 were born. 

Where a manufacturer's data sheet covers only single transistors, they tend to use only the original SOT 23 designation. Where a manufacturer is providing (let's say) diodes, diode pairs and diode triples in 3 and 6 pin versions of the SOT 23 package, they'll sometimes refer to the 3 pin version as SOT 23-3 to distinguish it from the SOT 23-6, but sometimes just call it SOT 23. It's up to the manufacturer. 

Note that SOT 23 and SOT 23-3 are just names, they don't have any definition. They have just entered the language through use and custom. JEDEC formally standardises dimensions, its TO-236AB package outline is the JEDEC title for what is known as SOT 23 and SOT 23-3.