The answer is—both.
As we have already seen, our Lord designated the Church established by Himself in the meridian of time as "My Church," that is to say, His Church—The Church of Jesus Christ. And, as also shown, when the Savior ministered in the resurrected state to the ancient inhabitants of America, He established His Church amongst them, and particularly directed that the institution be called by His name as the only properly descriptive title. See Book of Mormon, 3 Nephi 27.
When the Church was reestablished upon earth through the instrumentality of Joseph Smith the prophet, in 1830, it was provisionally called the Church of Jesus Christ, in harmony with the principle and practise established by the Savior among the Nephites, and to express the Lord's specific designation of the latter-day body as "My Church."
The early revelations given to the Church contain frequent mention of common consent or the voice of the members, as essential in matters of administration. The following excerpts are illustrative:
"No person is to be ordained to any office in this church, where there is a regularly organized branch of the same, without the vote of that church."
"And all things shall be done by common consent in the church, by much prayer and faith, for all things you shall receive by faith. Amen." (D&C 20 and 26.)
After the people had been trained through the revealed word and by actual experience in the affairs of Church government, when they had learned the basal lesson that upon every member rests a measure of responsibility, and that in consistency and justice each is entitled to part and voice in the activities of the organized body, the Lord specified in the following manner the expanded and complete name by which the institution was to be known. He spoke by revelation directed to the High Council and "unto all the elders and people of my Church of Jesus Christ of Latter-day Saints, scattered abroad in all the world. For thus shall my Church be called in the last days, even The Church of Jesus Christ of Latter-day Saints" (115:3-4).
The name thus conferred is a self-explanatory and exclusive title of distinction and authority. It is an epitome of the cardinal truths and of the philosophical basis of the system commonly called "Mormonism." Every prayer that is offered, every ordinance administered, every doctrine proclaimed by the Church, is voiced in the name of Him whose Church it is.
Nevertheless, as an association of human membership, as a working body having relation with the secular law, as a religious society claiming the rights of recognition and privilege common to all, it is the people's institution, for the operation of which, so far as such is dependent upon them, they are answerable to themselves, to the organization as a unit, and to God.
The plan of organization and government of the Church of Jesus Christ of Latter-day Saints is that of a theodemocracy, whose organic constitution has been revealed from heaven and is accepted by the members as their guide in faith, doctrine and practise.