Mythologically, the Aesir and the Vanir were described as two powerful tribes of gods, who went to war with one another, probably over the question of which tribe of gods could receive worship and offerings from humans. The war was ended by a peace treaty, and hostages were exchanged between the two sides. The Vanir received Hœnir and Mimir as hostages, while the Aesir received Njordr and Ingve/Freyr. Interestingly, Snorri's account in Ynglingasaga doesn't mention Freyja being sent as a hostage per se. She simply shows up among the Aesir, and is appointed to the post of high priestess of sacrifices. Her father and brother are similarly appointed as sacrificial priests.
But the key point here is that, mythologically, the Vanir disappear as a group after the death of Mimir. Assuming they are not simply known by a different name in the written sources*, our sole representatives of the Vanir tribe, Njord, Ingve/Freyr, and Freyja. And they are invariably referred to as Aesir in the written sources, after the point in mythological time when the Aesir-Vanir war is concluded, and they are integrated into Aesir society.
Whenever we are presented with lists of Aesir, Njord, Ingve/Freyr, and Freyja are included. Many have taken this to mean that the ON word Áss (plural Æsir) is somehow a generic term for divine beings. I think a much more likely interpretation of the usage here is that those three hostages did not retain their original Vanic identity, but were quickly absorbed into the Aesir tribe and assumed that tribal identity. As a chief example, when the Prose Edda introduces Ingve/Freyr and his sister Freyja, they are explicitly said to be of the Aesir:
Freyr is the most renowned of the Æsir; he rules over the rain and the shining of the sun, and therewithal the fruit of the earth; and it is good to call on him for fruitful seasons and peace. He governs also the prosperity of men. But Freyja is the most renowned of the goddesses... (Gylfaginning 24, Brodeur tr.)And in the original Old Norse, we can see that "goddesses" in the above is originally ásynjum, a female form of the ON word Æsir:
Freyr er inn ágætasti af ásum. Hann ræðr fyrir regni ok skini sólar ok þar með ávexti jarðar, ok á hann er gott at heita til árs ok friðar. Hann ræðr ok fésælu manna. En Freyja er ágætust af ásynjum.So in terms of the written lore, breaking out Njord, Ingve/Freyr, and Freyja into their own little sub-cult seems unwarranted. Once the war between the two tribes of gods is over, the Aesir take the stage and the three hostages are constantly and consistently referred to as being in their group, using that label. If nothing else, "Aesir" includes them, and so does the term "Asatru".
But a lot of people who like to make the distinction between the three Vanir** and the rest of the Aesir do so based on a false idea of their nature. All too often, we see the Vanir painted as pastoral gods of sex and plenty, forced to war only by the mean and terrible Aesir. In many ways, this hearkens back to the thoroughly-debunked theories of Marija Gimbutas, depicting peace-loving matriarchal earth-goddess-worshiping societies in prehistoric Europe conquered by mean sky-god-worshiping Indo-Europeans. It's complete horseshit historically speaking, but the image is still strong in many peoples' minds, especially those who come to Asatru from neopagan religions such as Wicca.
If nothing else, the written lore again comes to our aid in debunking this particular myth. The Vanir are said to be very powerful warriors, to the point of being able to throw down the walls of Asgard itself, and bring the Aesir to their knees. Freyja is a famous warrior, and equally famous for her ferocity. Not exactly peaceful traits. Ingve/Freyr is noted for a connection with wealth and prosperity, but so too are other Aesir; Odin's ring draupnir is a source of never-ending wealth, for instance, and Thor's hammer is famously used to bless the lap of the bride at weddings, presumably to invoke fertility; his connection with the rains that bring crops is also well-attested and obvious.
So, other than a focus on a particular trio of gods, there doesn't really seem much reason to differentiate the Vanir from the Aesir. And even then, those gods have long been called by the label Aesir, which would even be consistent with ancient Germanic kinship and tribal membership patterns. It's a bit of trendiness and a subtle "wonkier-than-thou" jab that serves no real purpose, and that we really don't need.
* Personally, I believe the Vanir to be the same as the Alfar, for a variety of reasons, but there is certainly no iron-clad evidence in favor of that view, and there is some evidence to argue against it. Perhaps I'll go over that in another post some day.
** The less said about the New Age whack-jobs who want to shanghai gods they happen to like into the Vanir, the better.