The fact that every person has a different personality is generally well accepted, but we sometimes "forget" this important fact when it comes to our own children. Not that it is forgotten per se, but we do wear our parenting lens when looking at them, and these lenses can be tinted, and biased.
Parents tend to describe their own children based on their own personality - the parent's own personality. For e.g. someone who is a result oriented Dominant (D) Style parent, describing a quiet introspective child who is a Concientious (C) Style child, may say "My kid is extremely quiet, doesn't like speaking up, and is very shy". This same child may be described by another C Style adult as "contemplative, likes gathering information and observing before speaking up, enjoys the company of her close friends". How one describes another is often tinted by your own personality style ... and we need to constantly remind ourselves that our perception is only our truth, and not everyone's truth.
Similarly, a Steady (S) Style parent who is not a party person may describe her party loving Influential (I) Style child, as being "loud, boisterous, drives me up the wall". Opposing personalities between a parent and child can be challenging. Its like driving through a brand new highway, with places that you have never seen, nor do you instinctively understand. But it makes for a great journey of learning, so long as we take time to understand the new place.
Each child is born with their own innate set of personalities, and as parents, its our job to understand their uniqueness, and not for the child to conform to the parents requirements. It is of course incredibly difficult especially for those who have children who are at opposite poles of personality styles, but acknowledging that they are their own unique personalities is already a good start. Remembering also that most people, your children included, are not deliberately doing something just to annoy you (though it may feel that way) will help replace judgement with acceptance.
Here are some key traits of the 4 personalities based on the theory of DISC personalities.
D (Dominant) style
Under pressure - strong willed, angry, rebellious
Sources of irritation - losing, weakness, lack of structure, lack of challenge
Motivated by - providing choices, ability to make decisions / lead
I (Influential) style
Under pressure - loud, active, attention seeking
Sources of irritation - routine, boredom, time constraints
Motivated by - opportunity to express thoughts, creative time
S (Steady) style
Under pressure - stubborn, passive aggressive
Sources of irritation - threat to stability or friendship, constant changes
Motivated by - opportunity to digest changes, close relationships, appreciation of loyalty
C (Conscientious) style
Under pressure - critical, worrisome, picky
Sources of irritation - incompetence, over exuberance, disorganisation
Motivated by - opportunity to research, provide rationale for actions
Finding out your child's and your personality styles together can be an eye opening experience for both of you. Despite how well you know your children, there is always something new you are able to learn, and learning it together is a great way to bond and address differences in a constructive, positive manner.