There are multiple dan scales. The KGS scale is an amateur dan scale. I don't know how much the scales overlap generally, but I'd imagine a 9 pro-dan professional to be somewhere around 12 dan on amateur scale (pro scales also have more dense scaling). However, the scales reach the ceiling at 9 dan by convention.
Even the abbreviations differ: 9d (amateur dan) vs 9p (pro dan).
KGS 9 dan players are pros or amateurs that are professional level like former insei. The highest rank is almost 11d (it still says 9d, but the graph goes even higher):
Even the abbreviations differ: 9d (amateur dan) vs 9p (pro dan).