The transmitter is included with the business version, which is why the price is higher.
Since the mouse has a Bluetooth connection for 3 different devices, the transmitter is not mandatory. Logitech itself says that the data protection (something like that) is very high thanks to the transmitter instead of just via Bluetooth.
I myself own version 3 and 3S. Also the very first version. The only difference is that the button on the 3S version doesn't have the typical clicking sound that you usually hear.

Hello,
In principle, not much. If you compare the products at Digitec, you have different product references:
3s : 910-006930
3s business: 910-006959

But if you type in the 2nd part number on the logitech website, this part number is not known. I assume that this is a mistake and that you can therefore buy the 3S without worrying.