From a British historic perspective the word “Forest” comes from the days of William the Conqueror, he brought the concept with him to the British Isles from the continent. It originally meant - the land that is protected by law… a kind of royal hunting grounds that protected the animals and the vegetation that supports the animals. It did not have to be forest in the modern sense of the word, but also moors, wetlands etc… it was the purpose of the land that got the name forest. Only royal hunting allowed, no-one else was allowed to use the forest.
Forest, the word, derives from Late Latin/Medieval Latin forestem silvam" the outside woods" and can be traced back to the days of Charlemagne (who interestingly enough was educated at the boys school next door to the girls school I attended as a teenager). It probably refers to the outside woods, ie those beyond the park or in other words the wilds beyond the cultivated. From this perspective forest is linked etymologically with the word foreign - outside. The word park has its ties with the word paddock (old English parrock/pearruc). The word silvam (silvis) above means woods. This words derives from silvaticus, which means wild... and is where the word savage has its roots.
Wudu (or widu) is the Old English word for tree or bean and has evolved into the word woods... it shares roots with the Swedish word "ved" which means firewood. The Swedish word for forest/wood is "skog" and is a very nordic word. It can be traced back to skogher and means "something that sticks up or shoots out", and over time what is a forest has changed... urskog is a forest that is untouched/unaffected by humans (virgin forest), then there is "kulturskog" (culture forest) where humans are very much a part of the forest, trädplantage (tree plantation) where the trees are planted and harvested and are, more often than not a monoculture, and then there is a naturskog (natural forest) where the forest has been spared from human greed for at least 150 years. In the last 20 years the forestry commission have included clearcuts as part of the forest (which having experienced clearcuts in "my" forest can emphatically say they do not feel like the forest).
Returning to the idea of forest being an area of land for hunting - there was aforestation, defining the land, ie not planting trees, but creating new boundaries, the actual reserve so to speak. Dis-aforestation was making the lands open to public use again… ie no longer reserved as a preservation for rich hunting grounds, but trees could be chopped, animals could graze, land could be farmed etc. So basically the word forest was about control. It did have a nice sustainable feel about it, protecting the ecosystem - but the purpose was a rich and diverse ecosystem, not disturbed by humans, so that the nig game would thrive and could be hunted by the King and friends. This meant vast areas of land were rendered out of bounds for people that had once been dependent on them. Not able to hunt, gather, collect wood etc. Just think of the tales of Robin Hood and Sherwood Forest and the people not being allowed to hunt for risk of imprisonment or death.
Indigenous peoples teach us that it is not humans that cause imbalance in nature. Living with nature can enhance it... after all we are a part of the ecosystem. The problem is human greed. Taking more than the ecosystem can sustain, and not allowing others to thrive - ie some take much more than their share and prevent others from having anything. Disconnecting from the woods could have been the start of the story that has seen most humans seeing them as something to be used, something that belongs to individuals, something other. Rather than something we belong to and have responsibility for.
The forests were massive areas. Hence why we probably feel that forest feels larger than woods. Woods or green wood were the words used rather than forest. Check our Forest Law, Charter of the Forest, Rime of King William and Magna Carta
References https://www.etymonline.com/word/forest