I'm under the impression that there is indeed a difference in authority between a ruling elder and a deacon, at least in the OPC, with the ruling elder having authority to use Scripture to exhort and correct. The deacon to use Scripture to edify and support/comfort. I used bold text to highlight the distinction between the pastor and the ruling elder, which sort of seem lumped together by that title up until the bolded text.
From the OPC
Book Of Church Order 2015 ;
In the case of a ruling elder :
The office of ruling elder is based upon the kingship of our Lord Jesus Christ, who provided for his church officers who should rule in his name. Paul and Barnabas “appointed . . . elders in every church”; and Paul commanded that those who “rule well be counted worthy of double honor, especially those who labor in the word and in teaching.” In this passage the Scriptures distinguish between elders who labor particularly in the Word and in doctrine—usually called ministers or pastors—
and elders who join with the minister in the government and discipline of the church—generally called ruling elders. It is the duty and privilege of ruling elders, in the name and by the authority of our ascended king, to rule over particular churches, and, as servants of our great shepherd, to care for his flock. Holy Scripture enjoins them: “Take heed unto yourselves, and to all the flock, in which the Holy Spirit hath made you bishops, to feed the church of God, which he purchased with his own blood.” As a consequence, ruling elders must be zealous in maintaining the purity of the ministration of the Word and sacraments. They must conscientiously exercise discipline and uphold the good order and peace of the church. With love and humility they should promote faithfulness on the part of both elders and deacons in the discharge of their duties. Moreover, they should have particular regard to the doctrine and conduct of the minister of the Word, in order that the church may be edified, and may manifest itself as the pillar and ground of the truth.
In the case of a deacon :
The office of deacon is based upon the solicitude and love of Christ for his own people. So tender is our Lord’s interest in their temporal needs that he considers what is done unto one of the least of his brethren as done unto him. For he will say to those who have ministered to his little ones: “I was hungry, and ye gave me to eat; I was thirsty, and ye gave me drink; I was a stranger, and ye took me in; naked, and ye clothed me; I was sick, and ye visited me; I was in prison, and ye came unto me.” In the beginning the apostles themselves ministered to the poor, but subsequently, in order that they might be able to devote themselves wholly to prayer and the ministry of the Word, they committed that responsibility to others, having directed the people to choose men of good report, full of the Holy Spirit and of wisdom. Since the days of the apostles the church has recognized the care of the poor as a distinct ministry of the church committed to deacons. The duties of deacons consist of encouraging members of the church to provide for those who are in want, seeking to prevent poverty, making discreet and cheerful distribution to the needy, praying with the distressed and reminding them of the consolations of Holy Scripture.