OBD just means On Board Diagnostics. It doesn't refer to a specific part.

The Engine Control Unit (ECU) from a '95 Civic is going to be different than the ECY from a '92 Integra. The plugs will be essentially the same but the program inside it will be different and there are certain connectors which are not shared. Each engine has its own unique ECU and if the motor was sold across OBD generations (from say, '94 to '01 like the 3rd-gen teg) there will be both an OBD1 and OBD2 ECU for that motor depending on which year the car it came from is.