Adoption is the giving to any one the name and place and privileges of a son who is not a son by birth. (1.) Natural. Thus Pharaoh's daughter adopted Moses (Ex 2:10), and Mordecai Esther (Es 2:7). (2.) National. God adopted Israel (Ex 4:22; De 7:6; Ho 11:1; Ro 9:4). (3.) Spiritual. An act of God's grace by which he brings men into the number of his redeemed family, and makes them partakers of all the blessings he has provided for them. Adoption represents the new relations into which the believer is introduced by justification, and the privileges connected therewith, viz., an interest in God's peculiar love (Joh 17:23; Ro 5:5-8), a spiritual nature (2Pe 1:4; Joh 1:13), the possession of a spirit becoming children of God (1Pe 1:14; 2Jo 1:13; Ro 8:15-21; Ga 5:1; Heb 2:15), present protection, consolation, supplies (Lu 12:27-32; Joh 14:18; 1Co 3:21-23; 2Co 1:4), fatherly chastisements (Heb 12:5-11), and a future glorious inheritance (Ro 8:17,23; Jas 2:5; Php 3:21).
Source: Easton's Bible Dictionary
Justification is the "judicial act whereby God imputes the righteousness of Christ to sinner" (p. 130). It is a declaration by God, not by works of man, in which the almighty declares sins freely pardoned and believers accounted righteous and worthy of eternal life. Justification involves a "change in the believer's standing before God rather than a change of nature" (p. 134). The grounds of the believer's new standing before God is Christ's righteousness which is imparted through the faith of the believer.
Reconcilation is a change from enmity to friendship. It is mutual, i.e., it is a change wrought in both parties who have been at enmity.
Sanctification involves more than a mere moral reformation of character, brought about by the power of the truth: it is the work of the Holy Spirit bringing the whole nature more and more under the influences of the new gracious principles implanted in the soul in regeneration. In other words, sanctification is the carrying on to perfection the work begun in regeneration, and it extends to the whole man (Ro 6:13; 2Co 4:6; Col 3:10; 1Jo 4:7; 1Co 6:19). It is the special office of the Holy Spirit in the plan of redemption to carry on this work (1Co 6:11; 2Th 2:13). Faith is instrumental in securing sanctification, inasmuch as it (1) secures union to Christ (Ga 2:20), and (2) brings the believer into living contact with the truth, whereby he is led to yield obedience "to the commands, trembling at the threatenings, and embracing the promises of God for this life and that which is to come."