Join/part messages are not sent on channels over 1,000 viewers, and there are also limitations to how they are sent, for example a join may not be sent until the user sends a message.
As for the chatter list on the Twitch site itself, the list states:
Some active viewers and chatters in the community.
So the public means of getting info on chatters wont be accurate. Where as the Get Chatters endpoint will be a more complete list of chatters and without the issues of using joins/parts.
To some degree it’s similar to how a channels subscribers is partially public in that sub badges when a user send chat messages indicates their subscriber status, but to get a full list of a broadcasters subscribers can only be obtained with their explicit consent to your app.