As grab said, they will form binds with everyone, but there is more to the key person. Certainly in preschool so two years plus.
I have just left on maternity leave, but my role as a key worker was to form a bound with a child. Get to know them, their likes/dislikes, what makes them happy and sad, get to know what they do outside of the setting.
Look at their learning, plan activities, group time, one to one to help move their learning on.
So if they come in never having held a pair of scissors, we look at fine motor skills, threading, hammer and nails, holding pens/pencils/scissors etc etc, building blocks.
This is for slightly older children, but we all work to the EYFS - early years foundation stage, which starts from birth, and moves all the way up to 60 months in Year R.
I'm guessing a nursery worker will use the basis of this, and most will produce some sort of paperwork that will show progress over the childs time with them. You can ask to see how they record your child's progress. Just remember, it varies from child to child, and setting to setting as to what they do.
OFSTED require every setting to keep some sort of record.
As long as your child is happy, has a variety of stimulation and continuous care that's good.