If I have two boards connected via RS422, do the same transceiver ICs have to be used at either side, or is it sufficient to have logic level voltages be the same even using different model ICs?
Neither the transceivers nor the logic levels need to be identical.
The RS-422 standard requires that transmitters must be able to generate a differential output voltage of at least ±2 V over a 100 Ω load. (And that receivers must be able to handle at least ±200 mV.) All 3.3 V and 5 V transceivers can handle this.
They can interface with each other, since RS-422 is the standard.
That said, different transceivers can have varying levels of speed, noise immunity, fault tolerance, drive capability (number of devices) etc. So although all transceivers will meet a baseline compatibility, they are not necessarily interchangeable or functional in all setups.