I have heard both usages. I guess that they are the same thing but wasn't exactly sure.
"Codes" are errors that are set when a problem is detected, typically affecting emissions.
"incomplete monitors" are tests that have not fully run to verify the validity of certain systems - perhaps HO2S, EVAP, catalyst, etc.
An incomplete monitor is not saying there's a problem; it's just indicating that the ECU has not been driven through a complete drive cycle to verify the validity of the tests. It doesn't pass an emissions inspection, but it doesn't fail either.