Are there a terms for difference sizes of log?

There are at least 2 kinds of trunk. A large, full-grown tree that could be able to be processed into lumber. And a smaller one, the size of branch of the full grown tree, but larger than a twig, that would be used as fence or pole or many products as-is without much processing.

I would call the large one as a log, in my opinion if it was thicker than human body it is surely a log. But I got uncomfortable calling the small sized ones logs, especially if they're around the size of a human leg. But it is still a trunk and not a branch so I couldn't call it a branch, right?

Does English have specific terms for these differences?

American English has 'cord wood;' lengths of trunk or limb stacked for fuel. But when those are sawn to fit the stove they are called(UK) logs and sit in a log-basket beside the fire. What you call logs would probably be called timber(UK), sent to a timber yard to be sawn and seasoned/ kiln dried/ processed.