There was for a while some fairly common rhetoric, even among OTO initiates of high degree, that attempted to differentiate between A.'.A.'. and OTO by calling the former a "teaching order" and the latter a "fraternal order." These etic yet vague designations are inefficient and counterproductive in my opinion. They do not change the fact that both orders provide instruction in their own ways, and both offer their own adumbrations of the Mystery of Universal Brotherhood.
The OTO does not "teach the secrets" in precisely the same way that the A.'.A.'. does not communicate either the knowledge or the power to achieve initiation. It is a preliminary disclaimer indicating that access to the teachings of the Order is not a sufficient condition to realize the attainments to which they are directed. The organized, persistent and applied will of the aspirant is the element most necessary.
Additionally, of course, OTO largely lacks the basis of "examination" purportedly used in grade advancement by the A.'.A.'. US NGMG Sabazius has explicitly written that OTO degrees are not seals on attainment, but rather opportunities for attainment. Those opportunities consist largely of teachings in dramatic form, as well as prescribed materials for study and practice, and various fora for instructions and experiments outside of the Order's canonical rites.