1: ἀπόλλυμι
(Strong's #622 — Verb — apollumi — ap-ol'-loo-mee )

signifies (I) In the Active Voice, (a) "to destroy, destroy utterly, kill," e.g., Matthew 10:28; Mark 1:24; 9:22; (b) "to lose utterly," e.g., Matthew 10:42 , of "losing" a reward; Luke 15:4 (1st part), of "losing" a sheep; Luke 9:25 , of "losing" oneself (of the "loss" of well-being hereafter); metaphorically, John 6:39 , of failing to save; John 18:9 , of Christ's not "losing" His own; (II) in the Middle Voice, (a) "to perish," of things, e.g., John 6:12 "(that nothing) be lost;" of persons, e.g., Matthew 8:25 , "we perish;" of the "loss" of eternal life, usually (always in the RV) translated to perish, John 3:16; 17:12 , AV, "is lost," RV, "perished;" 2—Corinthians 4:3 , "are perishing," AV, "are lost" (see PERISH); (b) "to be lost," e.g., Luke 15:4 (2nd part), "which is lost;" metaphorically, from the relation between shepherd and flock, of spiritual destitution and alienation from God, Matthew 10:6 , "(the) lost (sheep)" of the house of Israel; Luke 19:10 (the perfect tense translated "lost" is here intransitive). See DESTROY.

2: ζημιόω
(Strong's #2210 — Verb — zemioo — dzay-mee-o'-o )

"to damage" (akin to zemia, "damage," e.g., Acts 27:10,21 ), is used in the NT, in the Passive Voice, signifying "to suffer loss, forfeit, lose," Matthew 16:26; Mark 8:36 , of losing one's soul or life; Luke 9:25 , RV, "forfeit (his own self)," AV, "be cast away" (for the preceding verb see No. 1); 1—Corinthians 3:15 , "he shall suffer loss," i.e., at the Judgment-Seat of Christ (see 1—Corinthians 3:13 with 2—Corinthians 5:10 ); 2—Corinthians 7:9 , "(that) ye might suffer loss," RV (AV, "might receive damage"); though the Apostle did regret the necessity of making them sorry by his letter, he rejoiced that they were made sorry after a godly sort, and that they thus suffered no spiritual loss, which they would have done had their sorrow been otherwise than after a godly manner; in Philippians 3:8 , "I suffered the loss (of all things)," RV, i.e., of all things which he formerly counted gain (especially those in verses Philippians 3:5,6 , to which the article before "all things" points). See CAST , FORFEIT.