Not only are the refrigerants different, the lubricating oils in the refrigerant lines to lubricate the compressor are different, too. R12 uses mineral oil. R134 uses polyalkylene glycol (PAG).
If you convert from R12 to R134, any parts that are retained for re-use must be thoroughly flushed with an appropriate solvent to remove all the mineral oil, something that will cut and remove the mineral oil without damaging the parts.
About 25-30 years ago I converted the A/C system in a 1993 Ford Crown Victoria to R134. The kit came with everything except the evaporator. Since I didn't replace it (buried inside the dashboard) I flushed it with some kind of alcohol and blew out the alcohol with compressed air. I don't remember what alcohol I used. The conversion worked well, and it was still cooling when we sold the car in 2006.