On the side of one of the mounting flanges it should be stamped with "TD 42U". Only the 92-95 Civic Si and Civic VX use this distributor (all 91-94 JDM single cam D series VTEC and VTEC-E engines). There is no other distributor application that will work for the OBD1 D series VTEC engines.
You can mount up a non VTEC distributor but the ignition timing will be off by a lot even after you've maxed out the adjustment. It will run but get poor mileage, bad emissions, and low power. If one flange isn't bolted up, this indicates your idiot mechanic attempted to mount it improperly to set the ignition timing; however, the internal sensors are out of phase and you'll need to get the correct distributor.
The coil and ignitor inside the distributor are maintenance items that fail fairly commonly. You should not replace the entire distributor unless it leaks and replacing the O-ring doesn't fix the leak indicating that the shaft bearings are bad and it is wobbling. The CEL does not come on when the coil or ignitor fails.
It's possible that using the wrong distributor could lead to the problems described, but a proper diagnosis would have to be carried out AFTER the correct distributor is installed (if the issues persist) to know for sure.