Please don't be confused.
Engines can be equipped with an ECU. The ECU may control fuel intake, ignition etc.
ECU managed engines can still not have fuel injectors, and mix air-fuel beforehand and send it through the intake valves.
Fuel injectors are miniscule openings which present very high velocity, low pressure (nozzle) fuel intake so that turbulence is achieved more easily to a required degree for better output and more complete combustion. In this case the intake valves only intake air. This is in accordance with the thermodynamic philosophy that working substance in the engine is air (this phenomenon can truly be observed only in external combustion aka steam engines), and fuel is just a source of energy.
Traditionally diesel engines have always used fuel injectors. In petrol engines fuel injection was difficult because of knocking, preignition etc. But with the advent of electronics, engineers found a way to better control the fuel characteristics, and hence electronic fuel injection came into existence.
If I remember correctly, some old (1970s) mercedes and porsche engines had ECUs (for fuel metering) but mixed air-fuel the traditional way.
Also, you can see the new cultus engine, it has electronic fuel INJECTION but also has a distributor, meaning that fuel IGNITION is not electronic. Its still mechanically controlled (which is not at all bad since mechanical systems are also pretty reliable, I hate electronics obsessed people).
So, fuel metering, mixing and ignition can all either be done electronically or mechanically. Its not necessary to have an electronic system to control injection, but is otherwise very difficult in finer fuels.
Remember, electronic engine management and injection of fuel is different. EFI is the name of combining these two for fuel intake.