Class 1: A class 1 fax modem is little more than a data modem that has a very basic fax command set for handling group 3 fax transmissions. Because of this, the application software has to control all the data flow between the fax modem and the remote fax device.
Class 1.0: is exactly the same as Class 1 (above). The ITU recommended to change the name of the Class 1 fax command set to Class 1.0 for a common naming convention.
Class 2: Class 2 is a higher level specification than class 1. More of the fax protocol work is done within the fax modem firmware. This fax service class specification was never formally approved by the ITU. Every modem manufacturer is left to implement any command set of Class 2. This makes it difficult for application software to support all types of Class 2 fax modems.
Class 2.0: Class 2.0 is similar to the Class 2 specification that has been formally approved by the ITU. Every modem manufacturer have a basic Class 2.0 command set that has to be implemented in the firmware. The advantage of class 2/2.0 support over class 1/1.0 is that driving the modem does not hold up the PC with fax timing issues. This is particularly important in a multitasking environment and for network fax servers (as opposed to single user fax systems - where the user is often happy to wait for a fax to be transmitted).
The advantage of class 1/1.0 over class 2/2.0 is that the fax standard can be totally controlled by software rather than being dependent upon the quality of the fax firmware in the modem. Class 2.0 has the advantage over Class 2 that it has been formally documented and approved by the ITU. Hence, all class 2.0 devices should behave in the same way. Although Class 2 devices lack this uniformity they have been in use many years longer than class 2.0 devices - and hence, generally, the fax modem firmware (and its software support) has settled over time to become much more stable and reliable.