Well, I can't speak of everything, of course, but honestly, the OTO can be much more casual than some people would expect (at least in our lodge XD ). I see it mostly as an occultism-inclined book club with some group rituals and ceremonies here and there.
Well, it's important to know that most occult traditions are somewhat founded upon myths. Wicca's founder, Gardner, came up with that story about how he was thought in some witch coven....but in reality, his system is mostly inspired by Crowley/freemasonry initiatory systems and European pagan religions. In the end, Wicca ended up being quite similar to a religious system, with devotion to divinities and all that.
Traditional witchcraft is a bit more vague as it relates to a modern system of witchcraft that claims to be truer to actual European medieval witchcraft. It is not one single system, but a collection of practices, currents and mythos that are informed by both folk lore about witchcraft (a lot of them coming from writings about and during the witch-hunts, like the Devil and witches sabbath), archeologic evidence and texts, and from little known local spiritual practices still alive today. Most often than not, traditional witchcraft is not about religious practice, but about witchcraft practice. Aside from the more practical workings, traditional witchcraf is less religious than Wicca, but more mystical, or gnostic. Then again, as I said, there is many movements and not all of them share the same methods or goals.
More often than not, traditional witchcraft (often called ''The Craft'' ) practitioners don't distance themselves from the darker aspect of the world and self. The Wiccan motto ''Do what you will, so long as it harms none'' has little relevance to people of the Craft, and they will often criticize Wicca for sanitizing what is supposed to be an adversarial practice. That is not to mean that all traditional craft traditions are of the edgy satanic kind... Instead, though many would refute the label, traditional craft is closer to a ''grey'' system of magic.
Some of the most well-know modern currents are the Clan of Tubal Cain and the Cultus Sabatti.
If you are interested, Xoanon, the publishers of Cultus Sabatti's documentations have this article about their view of the Craft:
http://xoanon.co.uk/cultus-sabbati/