FRIEND
Christ's friends are those given Him of the Father (Doctrine & Covenants 84:63)
--- This one is the same definition as His sheep from John 10:27-29
His friends have an inheritance with Him (Doctrine & Covenants 93:45)
Jesus gave His life for His friends (John 15:13)
--- This one also seems the same as the seed of Christ from Mosiah 15:11-12
We are His friends if we do whatsover He commands (John 15:14)
--- This seems to be connected with LOVE (John 14:15), which disciple is also connected with (see below)
Friends are greater than servants, because He makes all things known to them (John 15:15)
Friends are gifted the Holy Spirit of Promise (Doctrine & Covenants 88:3)
Friends preach the gospel in His power (Doctrine & Covenants 84:77)
--- This one is like Christ's seed in Mosiah 15:14
DISCIPLE
His disciples love Him more than their own family members (Luke 14:26)
His disciples are His brother, sister, mother (Matthew 12:49)
--- This seems to be greater than servants (like friends)
His disciples do the will of the Father (Matthew 12:50)
His disciples take up their cross (crucify the natural man) (Luke 14:27)
His disciples forsake all they hath (Luke 14:33)
His disciples receive witness of the Father (John 6:65-66)
His disciples have love for each other as Jesus has for them (John 13:34-35)
His disciples continue in His word (John 8:31)
--- This one sounds to me like doing whatsoever He commands (like friends, in John 15:14)
His disciples abide in Him and His words abide in them (John 15:7-8)
His disciples ask what they will and it is done (John 15:7)
His disciples glorify the Father by bearing much fruit (John 15:8)
Jesus shows Himself unto His disciples (John 21:1)
--- I might be reading too much into the verse
We could also say His disciples walk with Him.
His disciples are a light unto people (3 Nephi 15:12)
His disciples speak the words of Christ (Ether 4:10)
His disciples partake of the Sacrament in remembrance (3 Nephi 18:7-8)
CONCLUSIONS
Well, I think one could surmise that His Friend is His disciple is His sheep is His seed.
What do you think?