Don't get too wrapped around the axle with the terminology. The inspector is using the generic term for the hinged joint your knuckle is pivoting about.
Ball Joint isn't the correct name, but the inspection method is the same when looking for worn Knuckle Bearings or King Pins. You jack the vehicle up so the tire and knuckle assembly is unloaded from the weight of the vehicle and you try to lift the tire with a pinch bar between the ground and the tire. If there is any movement, other than tire side wall deflection, the Knuckle Bearings (king pins, ball joints, whatever) could be worn and need to be replaced. I say "could be", because this movement can also be loose wheel bearings. To confirm it is, or isn't wheel bearings: Jack up a front wheel just enough to clear the ground. Grab the top of the tire at 12 o'clock and shake it in and out like it owes you money. If there is any movement or cluncking, its wheel bearings. Once you get those properly torqued then look at the knuckle bearings again.
In the image above, the knuckle bearings are labeled 4561 1F.
To confirm, follow the inspection method above with a helper running the pinch bar and you can crawl under the rig to see what is/isn't moving.