The difference between a wood and a forest is rather like the difference between a sea and an ocean. Basically, in both cases, it is generally a question of size, as you suggest.
Chambers Dictionary...wood = a collection of more or less densely growing trees; a stretch of country supporting such growth.
forest = a large uncultivated tract of land covered with trees and undergrowth.
The only apparent difference is one of size, if you consider the words in those definitions.
In Britain, the agency known as the Forestry Commission has multi-thousands of acres of deliberately planted trees. On the other hand, nature programmes on TV are constantly showing us life in the tropical rainforests, which were certainly not deliberately planted!
It would seem, therefore, that a forest can be either natural or man-made. I'm not so sure whether a wood can be either. Having said that, I'd imagine that some of the great country houses had woods deliberately created around them in past times.