I am old enough to remember when starter batteries were measured in cca's.
What is this AH madness, need alternators that can generate enough eleccy to keep the bit'n'bobs going, and batteries that can start an engine then go back to sleep after a refreshing recharge, that takes about 30 seconds.
I am guessing that the battery needs to be disconnected so as to not add more load to the charger(?)
You're likely a part of the majority here!
CCA, DIN, EN, ETN are all standards that describe the attributes of a battery. The newest battery standard is the European Type Number - ETN.
CCA is a US SAE standard for Cold Cranking Amps. That's the number of Amps the battery can deliver over 30 seconds at 0 degrees Fahrenheit and remain above 7.2v minimum.
The others are contemporary standards that cover electrical performance plus factors like physical size and format, post location and type, etc.
Ah rating has always been in the background. It's the rate of current (A) delivery over a period of time (h). Simplistically, a (new) 100Ah rated battery can deliver 100 Amps for one hour, 1 Amp for 100 hours, or any combination in between.
For starting batteries CCA performance is more important than Ah. Lead-acid batteries are good as cranking batteries. They like a short deep current discharge followed by a top-up charge from the alternator. They don't perform as well in a house battery role where Ah performance is needed to supply current to a load at near-constant voltage over time. This is where newer chemistries like AGM and Lithium shine. They are much better at providing Ah than lead-acid batteries.
Modern cars with smaller stop-start engines (and geared starter motors with reduced current requirements) can use an AGM cranking battery because AGM is an adequate compromise of CCA and Ah performance. AGM has a longer cycle life than lead-acid so is well suited to constant stop-start duty.
Yuasa UK has a good primer on the various standards.
A guide to understanding battery specifications for automotive, motorcycle, leisure, marine and garden batteries
www.yuasa.co.uk
Edit: I missed the 2nd question.
An easy grab would be to say it's about liability but I did read a reference to say that the desulphation phase might not start or might switch to a bulk charge phase if a smart charger senses a current draw from the battery while it is being charged. That could be something as simple as the vehicle waking up during desulphation phase. I guess the only way a smart charger is guaranteed to have complete control and monitoring of the battery is if it is electrically disconnected or removed from the vehicle.
That's contrary to guidance elsewhere which says to charge an installed battery with the negative lead connected to an earth/ground point down-circuit of the battery sensor so the BMS is aware of the current inflow to the battery and can update the SOC % correctly.
I think this needs a much better explanation from a battery or charger manufacturer.