Hi Andy
Welcome to Rootschat 
Draper being the occupation - not another surname he was known as......
This is the family in 1881, which I guess you already have?
1881: 51 Frederick St - Bishop Wearmouth, SunderlandRG11 / Piece: 4998 / Folio: 50 / Page: 30
Head: Robert J SMITH 30, Draper, b Scotland
Wife: Annie SMITH 30, b Durham
Son: Henry SMITH 1, b Bishop Wearmouth Durham
Son: Robert J SMITH 5 mths, b Bishop Wearmouth Durham
Mother: Agnes SMITH 60, married, b Scotland
Brother: Samuel SMITH 26, unm, Draper, b Scotland
Note: Samuel is not 36 in this Census - he's written down 26 - born abt 1854/55
Robert J SMITH & his wife Annie F SMITH & children are still in Bishop Wearmouth 1891.
MARRIAGE : Sunderland Jun Qtr 1879, 10a pg 593
Robert John SMITH & Ann Frances DAVIDSON on same page
By 1901, Annie is a widow with her children, in Durham.
DEATH: Robert J SMITH age 48
Sunderland Mar Qtr 1898 - 10a - pg311
Is there a particular reason you've posted this topic in the Aberdeen board - ie: do you have some indications the family was from Aberdeen?
Cheers
AMBLY