From what I can make out, there are some differences between Championship and Tournament greens. Not so obvious at first glance though.
My two penneth.
If you approach a green with little or no bs - on a championship green the ball is likely to run past the hole further than you may have been used too on tournies.
Also, you can see the difference on longer putts, putting downhill. If you set it up as a tournament green putt from 20ft+ away you will see the ball go a fair way past.
The same with chip, flops, pitches around the green. You need to play the same shot as before, but take care to apply the brakes a little more than you used to.
I might reevaluate this as I play more Alt with tour legends.
Experienced Tour Legends will be able to confirm whether I have this right or not.
Where you won't see much difference is under 12 feet putts on a flattish bit of green. At Tour Legend level hopefully many/most of your approaches land within this range.