Slave is the literal meaning of the word, doulos.
The first word used for service is diakanos, which means a minister to others in any usual way or work: but the word doulos means a bond slave, and the Lord here plainly teaches us that the highest service is that of a bond slave.
He Himself made Himself the servant of all, and he who would come nearest to Him and stand closest to Him at last, must likewise learn the spirit of the ministry that has utterly renounced selfish rights and claims forever.
It is quite possible to be entirely loyal to the Lord Jesus, and yet for Jesus' sake, a servant ourselves, and under the authority of those who are over us in the Lord.
The doulos spirit is the spirit of self-renunciation and glad submission to proper authority, service utterly disinterested, yielding our own preferences and interests unreservedly for the glory of the Master and the sake of our brethren. Lord, clothe us with humility and make us wholly Thine.