Vaccinations are the same for both calves. The calf that was rejected may not have gotten colostrum. - the first milk after partum. The first milk is high in antibodies which transfers the cows immunity to the calf.
At 34 days you are in a kind of vaccination hiatus. Some vaccination protocols require vaccination in the first 24 hours, for example Inforce 3 and First Defense. Other vaccinations are given when the calf is older.
At 34 days, I would give Pulmo Guard PHM -1 to protect from bacterial pneumonia. You can still give Inforce 3 to protect for viral respiratory diseases IBR, PI3 and BRSV.
I don't give the Clostridial vaccine such as a Blackleg 7 or 8 way until they are 90 days old.
I would make sure you have one of the oxytetracycline bolus products such as Oxy 500 Calf Bolus to treat scours. E. coli is the most common cause of scours here and in most places. An oxytetracycline bolus will treat that. If the calf that was rejected is well cared for, it still has an excellent chance of survival.