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update dutyrostershift

set dutyrostershift.savedduty_id = savedduty.id

from savedduty

where dutyrostershift.vacationtype = savedduty.name;

One thing worth pointing out is that savedduty.name is a varchar(20) and dutyrostershift.vacationtype is a varchar(50), meaning that one field could have values longer than the other and won't be updated. The above update statement will perform correctly, but it might miss some because the values can't match if dutyrostershift.vacationtype is longer than 20.