It is actually from verse 15 that Moses begins to speak prophetically of what God will do. Verse 15 says:
"The Lord thy God will raise up unto thee a Prophet from the midst of
thee, of thy brethren, like unto me; unto him ye shall hearken." The
Companion Bible p. 264
Then verse 18 reiterates the prophetic promise, adding a bit more information, along with verse 19:
"I will raise them up a Prophet from among their brethren, like unto
thee, and will put My words in His mouth; and he shall speak them unto
them all that I shall command Him. And it shall come to pass, that
whosoever will not hearken unto My words which He shall speak in My
name, I will require it of him." Ibid. vss. 18, 19
Note how Moses is speaking in verse 15, but God is speaking in verse 18 (at Horeb)? And it is also to be noted that there is more than one way in which Christ is likened unto Moses.
One similarity lies in human descent. Both were descended in the flesh from Abraham and (ultimately) from the first man, Adam. Christ is called the second man and the last Adam, which Moses never was. That is a point of superiority of Christ over Moses.
Another similarity lies in God's command that his people listen both to Moses, and to the future Prophet like Moses. Recall how those who started to resist Moses as God's anointed one, rebelling against him, were struck down? And those who resist Christ, the anointed one, and who rebel against him will also be struck down. That warning is in the Bible here:
"He that despiseth Moses' law died without mercy under two or three
witnesses: Of how much sorer punishment suppose ye shall he be thought
worthy, who hath trodden under foot the Son of God, and hath counted
the blood of the covenant, wherewith He was sanctified, an unholy
thing, and hath done despite unto the Spirit of grace?" Ibid.
Both enacted the Passover and the sprinkling of blood - Moses for the very first time as a symbol that set the obedient people free; Jesus with his own blood to set free all those to be brought into the new covenant in his blood. Christ was, himself, the sacrificial Lamb.
Both were called by God out of Egypt, to lead God's people away from worldly paganism into a wilderness (literal with Moses, spiritual with Jesus) prior to entering a 'Promised land'. Moses esteemed the reproaches of Christ greater riches than the treasures in Egypt... By faith he forsook Egypt..." (Hebrews 11:23-27).
Moses led the people through the waters of the Red Sea, parted by God. It was like a symbolic baptism that saved their physical lives. Christians are symbolically baptised into Jesus' death and raised to newness of life by his resurrection.
Moses gave the law at Mount Sinai, delivered by angels. Jesus fulfilled the law, nailing it ('the handwritten ordinance') to the cross - Colossians 2:14
No wonder Moses appeared with the transfigured Christ on the mountain (Horeb)! Moses represented the law, and Christ the fulfilment of it. Again, this demonstrates the superiority of Christ over Moses, though neither are to be despised. As the Bible explains regarding this, in the days of Moses there was grace (Exodus 34:6-7) and the law itself was an exhibition of truth, but when Jesus came, he was himself The Truth (John 14:6), and his life and death were the supreme manifestation of grace.
"For the law was given by Moses, but grace and truth came by Jesus
Christ." Ibid. John 1:17
That is not an exhaustive list, but it is what I can detail off the cuff.