A "normal" airline training program has a programed number of hours of ground school, broken down into so many hours of aircraft systems, so many hours CRM, so many HazMat, etc. That's going to be the same PIC, F/O or F/E. Then there will be a flight training syllabus, say 5 sims and checkride. There are a couple extra things on the PIC checkride but pretty much the same. Then the training program may have a LOFT segment. At this point the crewmember would receive the rating on their certificate. Then in the 121 world there is a matrix of required hours of operating experience depending on whether the crewmember is PIC, F/O or F/E and whether it is initial, transition or upgrade training. The OE is under the supervision of a Line Check Airman. At the end of the OE, the PIC receives a Line Check, which is different from the PC check in the sim. Then and only then is the crewmember "turned loose."
I have no idea what "type conversion" converts into in the US system but when the F/O's ground school is complete, when their flight training has been completed and they've passed their checkride, then they go fly line flights with a Check Airman.