Yes even Asatru has its differnt forms of belifs.
Theres Modernest,Folkish and some related forms of the religion.
Modernists feel any one who is a beliver in the Gods of Asgard my be Asatru.
Folkish belivers feel only those who are basicly Northen European decent can be real belivers but many of these groups do adopt into there Kindreds others if they like and accept them.
Some have confused this with racism but most folkish belivers are not racist.However as in any group large or small there are those who indead are racist.
Related Groups
These fine folks usaly follw at least one or more of the Norse Gods.
Here is a list of a few I know of.
Norse Wicca/pagans
Are mainly your average Wiccan who have chosen to incorparate the Norse gods into wicca.As Most Asatru do not practice Ritual or true magic.
Odinism
The term Odinism was coined by Orestes Brownson in 1848, in his book A revival of Odinism, or the old Scandinavian heathenism. The term was re-introduced in the late 1930s by Alexander Rud Mills in Australia with his First Anglecyn Church of Odin and his book The Call of Our ancient Nordic Religion. In the 1960s and early 1970s, Else Christensen's Odinist Study Group and later with the Odinist Fellowship brought the term into usage in North America. In the UK, the Odinic Rite has specifically identified themselves as "Odinists" since the 1970s, and is the longest running group to do so. Odinists do not necessarily focus on the worship of Odin and most honour the full pantheon
Theodism
Theodism, or Þéodisc Geléafa seeks to reconstruct the beliefs and practices of the Anglo-Saxon tribes which settled in England. þéodisc is the adjective of þéod "people, tribe", cognate to deutsch. As it evolved, the Theodish community moved past solely Anglo-Saxon forms and other Germanic tribal groups were also being reconstituted; Theodism, in this larger sense, now encompass groups practicing tribal beliefs from Scandinavia and the Continent, following in the model set forth by the Anglo Saxon theods founded in the 1970s. The term Theodism now encompasses Norman, Frisian, Angle, Saxon, Jutish, Gothic, Alemannic, Swedish and Danish tribal cultures. This relaxing of the original term "Theodism" functionally identifies Germanic neopagans who practice or advocate Neo-Tribalism.
Forn Sed
Old Norse Forn Siðr, Anglo-Saxon Fyrnsidu and its modern Scandinavian analogues Forn Sed, all meaning "Old Custom", is used as a term for pre-Christian Germanic culture in general, and for Germanic neopaganism in particular, mostly by groups in Scandinavia. Old Norse forn "old" is cognate to Sanskrit purana, English far. Old Norse siðr "custom" (not to be confused with sīðr "late"), Anglo-Saxon sidu, seodu "custom", cognate to Greek ethos, in the sense of "traditional law, way of life, proper behaviour". In meaning, the term corresponds exactly to Sanskrit sanātana dharma, the native term for Hinduism. In contradistinction to Ásatrú, inn forni siðr is actually attested in Old Norse, contrasting with inn nýi siðr "the new custom", and similarly Heiðinn siðr, contrasting with Kristinn siðr, and í fornum sið "in old (heathen) times"
Vanatru
They follow mainly the Vanir family of Gods .