Concise Bible Dictionary:
Three Hebrew words are translated “eternal.”
1. ad, very often translated “forever,” and with another word, olam, “forever and ever.” “The Lord shall reign forever and ever” (Ex. 15:18). “The Lord is king forever and ever” (Psa. 10:16: Compare also Psa. 45:6; Psa. 48:14; Psa. 52:8; Mic. 4:5). Ad is also translated “everlasting:” “the everlasting Father,” or “Father of the everlasting age” (Isa. 9:6). Also “eternity”; “the high and lofty One that inhabiteth eternity” (Isa. 57:15).
2. olam, signifying “everlasting,” “never ending.” It is often translated “forever:” “his mercy endureth forever” (1 Chron. 16:41); and “everlasting:” “the everlasting God” (Gen. 21:33; Psa. 90:2; Psa. 93:2; Psa. 103:17). “I will make thee an eternal excellency” (Isa. 60:15).
3. qedem, “ancient, that which is before.” “The eternal God is thy refuge” (Deut. 33:27). “Art thou not from everlasting?” (Hab. 1:12). “God is my King of old” (Psa. 74:12).
4. In the New Testament, ἀϊδιος, “perpetual:” occurs only in Romans 1:20, “his eternal power and Godhead”; and Jude 6, “reserved in everlasting chains.”
5. αἰών “age, duration, ever.” With a preposition “unto the ages” is often translated “forever”; and, when repeated, “forever and ever.” “He that eateth of this bread shall live forever” (John 6:58). “Christ abideth forever” (John 12:34). “To whom be glory forever and ever” (Gal. 1:5). “According to the eternal purpose” (Eph. 3:11). “Now unto the king eternal....be honor and glory forever and ever” (1 Tim. 1:17). This word is often translated “world,” but may at times be better rendered “age,” as “be not conformed to this age” (Rom. 12:2); and “forever and ever” may be translated “to the ages of ages,” though the meaning would be the same.
6. αἰώνιος, from αἰών, signifying “ever enduring.” It is always translated “eternal” or “everlasting,” except in Romans 16:25, “since the world began,” or “in the times of the ages” (2 Tim. 1:9; Titus 1:2); “before the world began,” or, “before the ages of time”; and Philemon 1:15, “forever.” This word is applied to God Himself as “the everlasting God” (Rom. 16:26); to the Holy Spirit (Heb. 9:14); to redemption (Heb. 9:12); inheritance (Heb. 9:15); salvation (Heb. 5:9); glory (1 Peter 5:10); and constantly to life (John 3:15-16, 36). On the other hand it is applied to punishment (Matt. 25:46); damnation (Mark 3:29); destruction (2 Thess. 1:9); and fire (Jude 7: Compare Isa. 33:14).
The above passages show that the same word is used for the existence of God Himself; for the salvation and blessedness of the saved; and for the punishment of the wicked.