In Matthew 11:28 we have the first word of the sentence, "Come." This is for salvation and the rest is to anyone who will receive it.
In Verse 29, the first word of the verse is "Take." This is our service to the Lord, involving another "rest"; which is experienced by being obedient.
Salvation. Matthew 11:28, "Come," no good works—just come by faith.
"Come unto me, all ye that labor and are heavy laden, and I will give you REST."
This is the "rest" of knowing you are saved and have eternal life. (John 3:16 and 1 John 5:13).
Service. Matthew 11:29,30. "Take my yoke," service and work.
"Take my yoke upon you, and learn of me: for I am meek and lowly in heart: and ye shall find REST unto your souls. For my yoke is easy, and my burden is light."
This is an additional "rest" experienced by the Christians who are doing their best in using their lives for the glory of the Lord.
Peace With God and The Peace of God
For additional study you may want to check Romans 5:1, where PEACE WITH GOD is spoken of concerning salvation. Compare this with the PEACE OF GOD; or our service to the Lord, as found in Philippians 4:5-7.