The issue outside of FAR 121 is business aircraft which do require a TR. The SIC training standards in FAR 61.55 are really quite "flexible" for being issued a SIC TR. The instructor, note instructor, no TRE, attests to training the applicant in aircraft systems, normal and emergency procedures, etc. The applicant for the SIC TR takes the application to the FSDO who issues the new license. Yes, many operators have both PICs and SICs complete the entire course and sim sessions together, it is NOT required for an SIC TR.
Check out FAR 61.55