I agree too but here's a bit more detail...
Not just west of Oxford, EA "registration" rules apply on all their water i.e. from the PLA boundary just below Teddington, all the way up to Lechlade, plus the last little bit of the Kennet at Reading including Blakes Lock. You pay at the first EA lock you come to where someone's on duty.
I think any powered leisure boat counts as a launch, and charges vary according to whether you buy a "day", week, month or year. Within that you pay by area in square metres, defined as length x beam, and the charge gets bigger according to what bracket your "area" falls into. You get two window stickers showing the expiry date, one for each side of your boat. No extra charge for air draught, but taller boats, or anyone who hasn't taken their chimney down, will have a real problem at Osney bridge in Oxford. Get that wrong and you'll feel "it hasn't been your day, your week, your month or even your year"!
If you are a commercial vessel carrying cargo (e.g. the NBT), very different rules apply (toll tickets based on weight of cargo and miles), and many of the lockkeepers don't fully understand how to issue them because there is not a lot of cargo carrying on the non tidal river. I have no idea what happens for the commercial passenger vessels, e.g. the big trip boats which operate at Windsor, but no doubt they have their own separate scale of charges.