Spirits are the living incarnations of ideas, concepts, and beliefs. Now, you can have spirits of a particular pine, or a spirit of all pines, or the spirit of all trees, or the spirit of all forests, or the spirit of the very concept of the wilderness itself. And it's not just physical things that have spirits: there are spirits of humour, spirits of math, spirits of language, spirits of politics, spirits of cooking, spirits of history, spirits of the arts, spirits of knowledge, spirits of death... you go down the list, and you'll find almost anything that humans can think about has a spirit attached to it.
Now, these spirits aren't always all that powerful... heck, many of them aren't even fully sentient. That tree spirit mentioned before? Unless that tree is of particular import to humans, it probably doesn't have a soul and is closer to a dog in terms of emotion and intellect than a human. But a forest probably has a name, a history, a mythology about it, and thus the spirit of that fore t is likely fully sentient, aware of itself and all those around it, acting as a shepherd for the various lesser spirits within its domain.
Spirits usually take their physical forms from whatever they're a spirit of. For a spirit of physical things, that's easy: a spirit of wolves appears as a large wolf with some odd fur patterns, a spirit of the forest appears as an old woman with skin of bark and moss for hair, a spirit of swords appears as a humanoid creature composed completely out of swords. Because spirits are tied into humanity, even the abstract spirits end up incarnating as something humans can relate to: a spirit of math might be a human completely composed of mathematical equations wrapping around themselves, a spirit of politics may appear as an idealized representation of someone who supports their ideology, a spirit of humour might appear as an archetypal comedian. Spirits don't really control all details of how they look, but they can nudge their forms in certain directions depending on their personalities.
After all, those spirits powerful enough to manifest full forms also have souls, and souls grant free will. A besouled spirit is capable of the full range of emotion, and of morality, as a human is. They can be just and kind, or wicked and cruel. A lot of times, this is shaped by their relationship with humanity. A spirit who incarnates something that has been abused by humanity--such as, say, the River Thames--is going to be a fair bit more spiteful than one who humanity reveres--say the spirit of ice cream, for example.
Also, like most supernaturals, the less powerful a particular spirit it, the more human it is--maybe not in form, but in personality and worldview. Sure, they're still the incarnation of a particular thing, but their worldview is small, local, relatable. The more powerful a spirit gets, the more alien and remote their worldview becomes--talking to the spirit of a particular forest is easy. Talking to the spirit of the idea of forests is probably going to give most folks a headache, and talking to the spirit of wilderness itself is something that could drive some people insane. At the very pinnacle of the hierarchy of spirits is the Anima Mundi, also known as Gaia, Mother Nature, Grandmother, or Eve. She is the only one of the five pillars of creation known to be sentient, and to have regular interactions with others--even down to lesser spirits and normal humans. She is immensely powerful, on the level that even the archangels at times defer to her wisdom, though as the spirit of the world, she doesn't tend to interfere in things unless the situation is incredibly dire.
Ghosts are a form of spirit--they are human souls who have come to incarnate the idea of themselves. In effect, when a human refuses to pass on to the Underworld after death, they have to find something to latch on to keep themselves whole--and that something is almost always themselves. So ghosts are both undead and spirit... which can be confusing at times, but nobody ever said the world was easy to understand.