I gonna be so honest bro I don't fully understand your question but Ima try help the best I can. Also the wiki hasn't been edited in a while from my knowledge so some things might be out of date.
First about colours, the genes in this game pretty much realism so it can be a bit confusing if you have never had experience (even with other animals) with how breeding for colours works. So if you click on a horses page then click the genetics icon below the horse image you should (if the horse has been gene tested) you should see both the color and genes sections. 
The color is what at the horse's current age is you can see visually with your eyes. 
The genes is the horse's genetic code. There is way too much for me to explain so there are many resources online where you can easily learn and read about how genetics work (even for horses).
The genes decide what a horse's colours are and the horse's parents (wild, foundation, and custom horses are rng basically) decided the horse's genes.
Now onto discplines or careers (I'll add on halter shows as well). So if you click on a horses page then click the graph icon below the horse image you should (if the horse has been personality tested/handled as a foal and is above the age of 2) you should see their performance stats (PS), skills, personality, and breed standards.
Base PS scores are decided by a horse's parents but you can train their scores. Base Skills are decided by a horse's parents and then experience in doing halter and career shows increase them. Personality and BS is based on a horse's parents.
If a horse has high PS scores in a certain discipline and a decent enough BS they will be good at disciplines. If a horse has good BS they will be good as a halter horse. If a horse's personality matches a certain career they will be good as a career horse.
Now here are my own personal beliefs on certain aspects of each one. Halter will earn you the most money but will cost the most, with career's being the opposite and disciplines being in between. Halter will increase your horse's level the most, with disciplines being the least but not by much. Halter requires the most energy with career requiring the least. Halter is the most popular with career being the least. Disciplines are the most widely available and easy to use with Halter and Career kinda of tied behind.
I personally recommend starting out by using disciplines then overtime you can figure out if careers or halters work better for you.

Again your question was slightly confusing and I know this post is old but I was bored and hope this helps.