Messiah is Hebrew and Christ is Greek. Also, what Moses wrote in the Law and what the prophets wrote were about Christ. (Jn 1:41,45)
Jn 1:41 He first findeth his own brother Simon, and saith unto him, We have found the Messias, which is, being interpreted, the Christ. 45 Philip findeth Nathanael, and saith unto him, We have found him, of whom Moses in the law, and the prophets, did write, Jesus of Nazareth, the son of Joseph.
The meaning of the Messiah is the Anointed. Then who are anointed in the old testament? kings, priests, and prophets were anointed.
(king, prophet) 1 Kings 19:16 And Jehu the son of Nimshi shalt thou anoint to be king over Israel: and Elisha the son of Shaphat of Abelmeholah shalt thou anoint to be prophet in thy room.
(priest) Ex 29:7 Then shalt thou take the anointing oil, and pour it upon his head, and anoint him.
"Jesus is the Christ" means that Jesus is the true King, and the true Priest, and the true Prophet.
Jesus is the true King, who broke Satan's head.( 1Jn 3:8)
1Jn 3:8 He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil.
Jesus is the true Priest, who died on the cross for forgiving our sins.(Mk 10:45)
Mk 10:45 For even the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many.
Jesus is the true Prophet, who is the way to meet God.(Jn 14:6)
Jn 14:6 Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
Jesus is the Christ, the anointed of God. (Acts 4:27)
Acts 4:27 For of a truth against thy holy child Jesus, whom thou hast anointed, both Herod, and Pontius Pilate, with the Gentiles, and the people of Israel, were gathered together,
Jesus finished the Christ job on the cross! (Jn 19:30)
Jn 19:30 When Jesus therefore had received the vinegar, he said, It is finished: and he bowed his head, and gave up the ghost.