Greetings,
First off, I would note that as a Confessional Lutheran, I do indeed believe, teach, and confess the Communion of the Saints. In some sense, even in oither communions with which I’m familiar, there is some appreciation for the unity of the Body of Christ in this world the next.
Perhaps, if I may clarify the intent of your question, are you attempting to distinguish what others believe about the role or function of the Communion of the Saints, both on earth and in heaven?
If this is your direction for the query, I’ll add my two cents.
Lutheran theology recognizes that the Scriptures speak very little about what the Saints do when they are brought into the presence of Almighty God in Christ. We have a few glimpses in St. John’s Apocalypse, and a few in the OT, and perhaps a couple more peppered throughout the NT and Apocrypha. Lutherans will generally confess that since there is no particular command or promise of Scripture regarding how we relate to our brothers and sisters who have entered the Church Triumphant, we generally do not bind consciences in this regard. By and large, it is a matter of private piety.
Some Lutherans will squirm with the idea of intercession by the Saints on our behalf… or petitioning our Blessed Mother and the Saints to pray for us to the Lord. I do not-- I think there is plenty of Church history and tradition to back up this pious practice, and I think it helps teach humility among the faithful. However, prayer is an act of faith, as should be all the Christian life… so I would never presume to make forced dogma out of a pious opinion. I know, however, from personal experience, that the prayers of Our Blessed Mother and the Saints have been heard and answered by our Lord, and I will not surrender my piety for the squeemishness of my other Lutheran friends (though I wouldn’t flaunt it to their distress, either.)
Grace and peace.