I have been looking at various ECUs trying to understand how they
work. 

Fortunately, I was on the phone, and Ed just saved me a lot of typing :-)   One additional note, ECU's can run in open loop, or closed loop modes.  Tracy's EC-2 is open loop all the time.  Basically, in open loop, you supply a pre-designated amount of fuel from a look-up table, and you trust that it's what you wanted.  When we tune the EC-2, we're making this look-up table.  In closed loop mode, you start with the look up table number, then check the O2 sensor to see how close you came.  The ECU can add or remove fuel as needed to hit a target O2 number.

Cars use closed loop whenever they can, or emissions and fuel efficiency, but they also run in open loop mode under certain conditions.  For example, you're car will run in open loop mode when you first start it, because there's no valid O2 sensor reading until it warms up.  Multi-wire heated O2 sensors have shortened this time considerably over the years.   I think most cars also run in open loop mode during full throttle operation.

Rusty