I am actually more interested in the definition of polytheism. This might be a dated view, but I understand polytheism to be very grounded in animism.
An example, is the Indigenous tribes of North America. They can all characterize as animistic traditions, each tribe (and each family) in its own context. But some tribes in the southwest additionally develop polytheistic traditions (where certain nature beings become perceived as supreme gods), and some tribes in the northeast additionally develop monotheistic (where a transcendent imageless creator brings all nature beings into existence).
The ancient Greeks used the term Nike for victory. As I understand it, this was both a goddess and an abstract term. To an ancient mind, pre-Platon, abstract concepts were not a natural thing. So to have a goddess representing an abstract term makes the term easier to grasp. Greek polytheism had goddesses from the abstract-concept Nike to the much more personalized gods like Zeus, Hera, and their ilk. I find that in this way, polytheism begins in something very similar to animism, with Nike being the "sky-man" equivalent of "victory-woman". Its funny that this trend with gods as manifestations of abstract concepts actually became more prevalent in Hellenistic culture, after Alexander the Great and the apex of Classical Greece. What I am trying to say is that the line between animism and polytheism is not at all clear.
Most polytheistic cultures preserve earlier animistic traditions to various degrees. (Most monotheistic cultures do too. For example, in Christianity, a church building itself or a Bible itself may be a holy entity, even when not actually worshiped.)
Polytheism essentially relates to some variation of a "lord-versus-servant" relationship. Where it appears, it typically emerges in the context of urbanization (such as various locales during the Bronze Age), where a local-monarch uses violence to assert political dominance, while a government administration consists of a bureaucracy of specialists who "serve" the local-monarch. Then the culture perceives a distinction between which natural feature is the "monarch", and which ones are "servants". Typically, there is a "priesthood" whose official occupation is to take care of a "temple", where the "god" inhabits.
The Greek worldview (in the sense of Hellenism) sees a "material world" and a "spiritual world" as two separate places, indeed, two separate modes of existence. For example, Platonism sees the spiritual world as eternal, and the material world as temporal. Related traditions characterize the spiritual aspect as "good" and the material aspect as "evil".
But this Greek dualism is alien to animism. In animism, the material objects themselves are living beings. Any "heaven" sotospeak is literally the sky where the clouds are. Likewise, any realm of the dead is underground where the graves are. When a human dies, they shapeshift into different natural features. Part of them is a corpse that disintegrates into the earth. Part of them is a breath that becomes part of the wind in the sky. Sámi shamanism has a mindful aspect that seems more transcendent than literal breath, yet the outofbody journey is still of the "breath" soul (vuoigŋa) that is part of a material world, traveling, and visiting places that are in the material world.
It is important to understand animism and why it, in itself, is neither polytheism nor monotheism.
A main clue is: animism is a horizontal relationship among family and neighbors, while polytheism is a vertical relationship among masters and servants. If there is an institution of a priesthood whose official job is to "serve" the sacred figures, it is probably polytheism. If humans are being literally killed and offered to the sacred figures, so that these figures are strictly and existentially more important than humans, it is almost certainly polytheism (or monotheism).