"Rest" in Matthew 11:28, 29

QUESTION: Says Jesus in Matt. 11:28, 29, "I will give you rest... and ye shall find rest." Is the "rest'" in both verses the same?

ANSWER: Some so teach. They are supported by the authority of Olshausen, a noted German exegete, who makes the rest given by Jesus the release from the burden of guilt by conscious forgiveness, and rest found under the yoke of guidance and discipline imposed by Christ, "the cessation of discord in man which is not immediately removed after his entering into the element of the good" — the state of the regenerate. It is a curious fact that the clause denoting the second rest is quoted from Jeremiah 6:16, "Ask for the old paths, where is the way; and walk therein, and ye shall find rest for your souls." This is the way the Hebrew reads, but if the quotation had been made from the LXX the Greek version quoted very often in the N.T. (ninety-nine times being in Matthew's Gospel), it would have been, "and ye shall find purification to your souls." This is the way the Hebrew reads, but it is the quotation from the Septuagist, because the word ἁγνισμός (hagnismos),  "purification," is used in the N. T. only once (Acts 21:26), and that is in a ceremonial sense descriptive of Paul's unwise attempt to conciliate the angry Jews by purifying himself in the Temple. Words in the course of centuries take on different shades of meaning. Christ kept as far as possible from teaching that mere ritualism can give soul rest. This comes only by crucifying "the flesh which lusteth against the Spirit," or by spiritual purification.

— Steele's Answers pp. 168, 169.