The Tortoise weighed 78 tonnes, and was a Heavy Assault Tank designed to take out heavily fortified positions such as concrete blockhouses. Apparently, a well thought out concept, its development was too late as the war ended, so there was no need to put them into production. This is the only one in existence, the others being blown to bits as targets for training.
My understanding, is that tanks are combat vehicles which work on line of sight, and so have to be mobile and heavily armoured. They usually have turrets, but not always.
SPGs are lightly armoured as they don't go into battle, but are mobile artillery pieces, that fire from well behind the front line, in groups, putting down bombardments up to 20 miles away. There eyes and ears are forward observers, who report back their success or not. Some SPGs don't even have a roof, but are open.
Tank Destroyers I'm not clear about. Low profile, huge gun, no turret, and the clues in the title.
I think that is a Canadian Ram in the background, Andy. And my understanding of the Archer, is that the British tanks were seriously under gunned with 40mm 2lbr pea shooters, so desperately needed to put a big gun on a tracked chassis, hence the Archer.
The Tank Museum at Bovington in Dorset, is probably my favourite museum of all. So far, I've spent three full days in there, and still have more to see. A few hours in there would only scratch the surface. They reckon, just with the existing stuff they have in storage, they've another 400 years worth of restoration!