1: ἱερεύς
(Strong's #2409 — Noun Masculine — hiereus — hee-er-yooce' )

"one who offers sacrifice and has the charge of things pertaining thereto," is used (a) of a "priest" of the pagan god Zeus, Acts 14:13; (b) of Jewish "priests," e.g., Matthew 8:4; 12:4,5; Luke 1:5 , where allusion is made to the 24 courses of "priests" appointed for service in the Temple (cp. 1—Chronicles 24:4 ff.); John 1:19; Hebrews 8:4; (c) of believers, Revelation 1:6; 5:10; 20:6 . Israel was primarily designed as a nation to be a kingdom of "priests," offering service to God, e.g., Exodus 19:6; the Israelites having renounced their obligations, Exodus 20:19 , the Aaronic priesthood was selected for the purpose, till Christ came to fulfil His ministry in offering up Himself; since then the Jewish priesthood has been abrogated, to be resumed nationally, on behalf of Gentiles, in the millenial kingdom, Is. 61:6; 66:21. Meanwhile all believers, from Jews and Gentiles, are constituted "a kingdom of priests," Revelation 1:6 (see above), "a holy priesthood," 1—Peter 2:5 , and "royal," 1—Peter 2:9 . The NT knows nothing of a sacerdotal class in contrast to the laity; all believers are commanded to offer the sacrifices mentioned in Romans 12:1; Philippians 2:17; 4:18; Hebrews 13:15,16; 1—Peter 2:5; (d) of Christ, Hebrews 5:6; 7:11,15,17,21; 8:4 (negatively); (e) of Melchizedek, as the forshadower of Christ, Hebrews 7:1,3 .

2: ἀρχιερεύς
(Strong's #749 — Noun Masculine — archiereus — ar-khee-er-yuce' )

designates (a) "the high priests" of the Levitical order, frequently called "chief priests" in the NT, and including "ex-high priests" and members of "high priestly" families, e.g., Matthew 2:4; 16:21; 20:18; 21:15; in the singular, a "high priest," e.g., Abiathar, Mark 2:26; Annas and Caiaphas, Luke 3:2 , where the RV rightly has "in the high priesthood of A. and C." (cp. Acts 4:6 ). As to the combination of the two in this respect, Annas was the "high priest" from A.D. 7-14, and, by the time referred to, had been deposed for some years; his son-in-law, Caiaphas, the fourth "high priest" since his deposition, was appointed about A.D. 24. That Annas was still called the "high priest" is explained by the facts (1) that by the Mosaic law the high priesthood was held for life, Numbers 35:25; his deposition was the capricious act of the Roman procurator, but he would still be regarded legally and religiously as "high priest" by the Jews; (2) that he probably still held the office of deputy-president of the Sanhedrin (cp. 2—Kings 25:18 ); (3) that he was a man whose age, wealth and family connections gave him a preponderant influence, by which he held the real sacerdotal power; indeed at this time the high priesthood was in the hands of a clique of some half dozen families; the language of the writers of the Gospels is in accordance with this, in attributing the high priesthood rather to a caste than a person; (4) the "high priests" were at that period mere puppets of Roman authorities who deposed them at will, with the result that the title was used more loosely than in former days.

Leviticus 4:15,16Hebrews 5:1-48:39:7,25Hebrews 10:11Hebrews 4:155:5,106:207:268:1,3 Hebrews 4:14Hebrews 10:21Hebrews 2:17Hebrews 3:1Hebrews 5:10Hebrews 7:28Hebrews 5:6,10Hebrews 5:4,5Hebrews 2:1710:5Hebrews 8:39:12,14,27,2810:4-12Hebrews 4:148:29:11,12,2410:12,19Hebrews 2:184:157:258:69:15,24Acts 4:6