They are not the same thing, if you think about it. If submission is non-reciprocal, then the command in Eph. 5:21 is only intended for those Christians who are in roles of submission to other Christians, it is not an instruction for everyone. Some time ago after careful consideration, Denny Burk wrote,
I think “one another” is used in the non-reciprocal sense Ephesians 5:21 as well.But the other day he wrote about Thielman,
He takes a different tack on the interpretation of “submitting to one another” in verse 5:21. He understands that both husbands and wives are to submit to one another, but they are to do so in different ways. Thus he maintains the Pauline notion of headship while distinguishing his view from the “mutual submission” interpretation of egalitarians.For most complementarians, there are many different ways to interpret the words of scripture. As long as they all lead to the authority of the husband over the wife, one can still call oneself a complementarian. But great latitude is allowed in exegeting scripture. Why is Thielman acceptable? Because he distinguishes himself from egalitarians. Not because he has any particular understanding of scripture. In fact, relatively few jump to defend the clarity of scripture. Many jump to defend the authority of the male over the female.