If you live in a older house in the UK you will either have a Belfast or London version of this object...the "Belfast" is more widespread
What is it? and B) What's the difference in the designs

Is it one of those water closet toilets that is mounted way up the wall near the ceiling and you flush it by pulling a chain? And the Belfast model has a lock-on lid so no one can slip an explosive device into it in public washrooms? Or am I just reaching?

Babs
You are in the right area with your "Plumbing"
description (very warm)

Clue to location look in another room

"Or am I just reaching?"

Babs, you are edging out JR as Master (Mistress?) of the Bad Pun.
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Bedstor, I am guessing that the answer is a water heater. (That is what it is called here.)

So is it a geyser ?If it is, my guess is that one type ignites as soon as you turn the tap on, being operated by the water flow, and the other has to be ignited separately. Quaint to think that these devices became obsolete but we now have point heaters which work on the same principle but are used to heat the whole house's central heating as well as the hot water. These are up to the minute, state of the art, space-saving technology !

Keep going (and thanks Fred you've given me a good idea for another trivia question)
and the clue is its something concerned with water/plumbing

I think they are radiators..just a guess.

A Belfast is a type of sink. Don't know how it differs from a London one.It appears to be no more than the old deep ceramic kitchen sink: suddenly very trendy in retro-minded London. They've had the Aga stove (replaced many years ago by any sane householder who had no option back then but to have a range in their country cottage) and now they have the uselessly deep and big, rectangular, ceramic,heavy sink (replaced many years ago by...). My guess is that the Belfast has a central plug-hole and the London is shallower and has an edge plug-hole.

The difference Fred (and now you can show your skill) is the Belfast has an overflow and the London has none
And if course a proper Belfast/London is ceramic/rectangular

Here are pictures an descriptions of the types plus an "Edinburgh" variation on the Belfast (has a bowed front)

www.kitchensupplies.co.uk/acatalog/traditional_fireclay_sinks.html