Hello Hawkeye5!
The proper WOA is a finishing hone, at least equivalent to 10k.
The trouble with descriptions of old hones from this region stems from the fact that in the early days both the Tam O'Shanter and the Water of Ayr were called Water of Ayr stones.
To avoid confusion, the mine owner at the time - a Mr Kelly - paid for a nationwide advert in 1885 laying down a naming structure for hones (Tam O'Shanter, Dalmore Blue, etc) from his mine - Dalmore Quarry. Before this they were sold under the company name - The Water of Ayr Hone Works, and the company name was used for its products as is often the way. The differentiation between TOS and WOA hones stems from around this time, so earlier examples called WOA could be either TOA or WOA. Interestingly, the hone we now call WOA didn't even come from this mine - it came from another mine in Meikledale!
The fact that the one you are interested in mentions 'carpenters and joiners' leads me to think that it is in fact a TOA. It should say "For Razors, Scalpels or Very Fine Knives.'
I haven't seen different grades of WOA, but some of them do indeed look like Tams, but darker, drabber, less spotting - they aren't all a dark grey/blue colour with no speckles.
Regards,
Neil