This was a common view I ran across as well. I think because many Pagans come from Jewish or Christian (mostly Christian), it’s a reactionary thing. They think that “because I reject monotheism I must then therefore completely reject YHVH (or Jesus, or both)” when really what they’re rejecting is how monotheists perceive YHVH and Jesus.
It depends on who you ask. Some believe that belief is what keeps a deity going, so if everyone stopped believing in a certain deity, that deity would cease to exist (although, we still name companies after gods, and we tell their stories, so I wonder if that is not a “belief” of some sort). Others (particularly “hard polytheists”) will say that gods don’t depend on human belief to sustain them. It’s not uncommon to find Pagans (even in the same group) who have radically different views of deity and yet still manage to come together for rituals. Myself, I used to subscribe to the “gods have power through human belief” but now I’m more “gods don’t depend on humans for things” (although mythologically, the Sumerian pantheon depended on sacrifices for sustenance), but I think both positions have their benefits and drawbacks.
Asatru is specifically Icelandic reconstructionist Heathenry. There are other types of Heathenry (Heathenry, btw, is basically a catch-all term for reconstructionist Germanic Paganism) such as Anglo-Saxon Heathenry, Frankish Heathenry, Forn Siðr (Scandinavian Heathenry) and many others. I know we recently had a thread about the reliability of Wikipedia, but it does do a good job of listing different movements:
en.wikipedia.org/wiki/Germanic_Neopaganism
A major dividing line between Vanatru and other forms of Germanic Paganism is which gods we honour. Many Asatru honour both the Aesir (Odin, Thor, Tyr) and the Vanir (Njord, Freyja, Freyr), but they tend to honour the Aesir primarily and the Vanir secondarily. The loosest definition of someone who is “Vanatru” is “someone who has one of the Vanir as a patron, someone who worships the Vanir primarily and the Aesir secondarily, or someone who worships the Vanir exclusively”.
It’s difficult to come up with an exact analogy, but it’s almost like saying: “A Christian is someone who believes in and follows the teachings of Jesus.” Sort of.
The second big difference is that Vanic Pagans may or may not be reconstructionist in their approach to religion. Again, some will worship the Vanir in exactly the same way as someone who is a member of Asatru would, reasoning that, well, these deities were worshiped in that way historically. Others say that the surviving lore is largely focused on “important” deities like Odin and Tyr, whereas we only have a few stories about Freyr and his family, and that there were important differences in cultic practice and general behaviour (Snorri mentions that the Vanir practiced incest while the Aesir do not, the Aesir also seem much more concerned with adultery and such).
I think that basically what I’m trying to say is: “We have the same pantheon, but we have different ways of approaching that pantheon.”
Let’s see, some other differences:
I often call Vanatru “Asatru’s earth-based hippie cousin” because there does seem to be more of a focus on nature–whereas many Asatruar will LOUDLY proclaim that they’re “not an earth-based tradition” (which is, to some extent, true). This has to do in part with reconstructionist traditions trying to distance themselves from Wicca, which is probably the Pagan tradition that most people recognize.
This probably seems a little confusing because I’m throwing lots of terms and viewpoints around. First let me say that I don’t consider myself to be a reconstructionist, hence why I don’t refer to myself as a ‘Heathen’ (which tends to imply that one is a reconstructionist). I have my own issues with the way some of my fellow Pagans treat the written records and scholarship in general. I could probably go on, but I’d almost need another post to get all my thoughts down.