Perhaps reading the LDS Church Handbook of Instructions would be helpful:
lds.org/handbook/handbook-2-administering-the-church/relief-society?lang=eng
Some relevant quotes:
**
The Relief Society is an auxiliary to the priesthood. All auxiliary organizations exist to help Church members grow in their testimonies of Heavenly Father, Jesus Christ, and the restored gospel. Through the work of the auxiliaries, members receive instruction, encouragement, and support as they strive to live according to gospel principles.**
**Purposes
Relief Society prepares women for the blessings of eternal life by helping them increase their faith and personal righteousness, strengthen families and homes, and help those in need. Relief Society accomplishes these purposes through Sunday gospel instruction, other Relief Society meetings, visiting teaching, and welfare and compassionate service.
9.2 Ward Relief Society Leadership
Bishopric
The bishop and his counselors provide priesthood leadership for the Relief Society.
The bishop calls and sets apart a sister to serve as Relief Society president. He oversees the calling and setting apart of counselors in the ward Relief Society presidency, the ward Relief Society secretary, and other sisters who serve in Relief Society callings. He may assign his counselors to call and set apart these sisters.
The bishop meets with the Relief Society president regularly to discuss Relief Society and welfare matters.
Ward Relief Society Presidency
The Relief Society presidency consists of a president and two counselors. They are spiritual leaders in the effort to strengthen sisters and their families. They work under the direction of the bishopric. They also receive orientation and ongoing support from the stake Relief Society presidency.
Ward Relief Society President
The Relief Society president has the following responsibilities:
She serves as a member of the ward council. As a member of this council, she participates in efforts to build faith and strengthen individuals and families (see chapter 4).
She meets regularly with the bishop to report on and discuss Relief Society and welfare matters.
At the bishop’s request, she visits homes of members to evaluate welfare needs and suggest ways to respond to them (see 9.6.1). In the absence of the Relief Society president, the bishop may assign a counselor in the Relief Society presidency to respond to an urgent need.
She submits recommendations to the bishopric for sisters to be called to serve as leaders and teachers and to fulfill other callings in the Relief Society. In making these recommendations, she follows the guidelines in 19.1.1 and 19.1.2.
She coordinates ward Relief Society welfare efforts during emergencies.
She teaches other Relief Society leaders and teachers their duties, using this handbook as a resource.
She oversees the records, reports, budget, and finances of the ward Relief Society. The Relief Society secretary helps with this responsibility.
9.4.2
Additional Relief Society Meetings
Planning the Meetings
Relief Society leaders prayerfully counsel together about the topics that will strengthen sisters and their families and about the best ways to teach those topics.
The Relief Society president ensures that plans for all Relief Society meetings are approved by the bishop. She also ensures that all plans are in accordance with the guidelines in chapter 13.
9.8 Stake Relief Society Leadership
9.8.1
Stake Presidency
The stake president oversees the Relief Society in the stake. He meets regularly (usually monthly) with the stake Relief Society president or presidency. He provides priesthood direction as they counsel together about matters that pertain to Relief Society sisters and their families. These matters may include welfare needs, the progress and needs of sisters in the stake, and Relief Society meetings, instruction, and activities.
9.8.2
Stake Relief Society Presidency
The responsibilities of stake auxiliary presidencies are outlined in 15.4.1. The stake Relief Society presidency also has the following responsibilities:
Under the direction of the stake presidency, they may plan and carry out one or two stake Relief Society meetings each year for all Relief Society sisters in the stake. These meetings may include service, classes, projects, conferences, and workshops. One of them may be held in conjunction with the general Relief Society meeting. The stake Relief Society presidency may form committees to help as needed.**
I think that gives everyone an idea about what some were talking about in this thread as far as the relationship between the priesthood holders/leaders and the Relief Society.