This is just so common that dads and moms appear differently to other people at different places. The perception of people is different when it comes to the role of a dad vs. the role of a mother. If the same task done by a mother is done by a father then public opinions change and the way to see the doer of the task changes too.
To justify this, Chaunie Brusie, a freelance writer and a mother of four kids present 5 comical illustrations that reveal out the major variations between dads and moms when they are out in public. Have a look at these comics.