What is the difference between the Honeywell thermostats TH8320R1003 and TH8321WF1001 and TH8110R1008?

Excellent question because this is a source of much confusion. Especially because all 3 thermostats look identical! For a very complete answer Google Honeywell (now Resideo) document 50-1376 (the revision is on the bottom right hand corner, the latest as of December 2021 is 08/20). Here's a partial answer:

First, communication differences: The models with R in them are Redlink models. This means that they can be used as standalone thermostats or with a conjunction of Honeywell proprietary Redlink wireless accessories (remote temperature sensors, remote control modules, Zone panels, IAQ sensors, ethernet gateway for cloud/Wi-fi control, etc). An important point to consider is that, if used as standalone thermostats (with no Redlink accessories) they can be powered by batteries OR hardwired ('C'wire) and use the batteries as a backup. If used with accessories, including the gateway for Wi fi control, they need to be hardwired. The TH8321WF1001 is a Wi fi model. Needs to be hardwired (C wire) to operate. Does not communicate with any Redlink devices.
Next: Output and Input differences. here's what the digits indicate. The 2nd digit indicates the number of heat stages for a heat pump that it can handle- As an example with the TH83XXXX, in this case 3 heat stages for a heat pump(heat stages for conventional equipment are typically one fewer, because no backup heat- so in this case 2). The following digit indicates the number of cooling stages: in the case of the the TH832XXXX, 2 cooling stages. The third digit, if a "1" indicates it has a built in humidity sensor; a '0' means it doesn't. So the TH8321WF1001 is the only one of the models mentioned that has a humidity sensor. Hope that helped!