A — 1: ὁμολογέω
(Strong's #3670 — Verb — homologeo — hom-ol-og-eh'-o )

lit., "to speak the same thing" (homos, "same," lego, "to speak"), "to assent, accord, agree with," denotes, (a) "to confess, declare, admit," John 1:20; e.g., Acts 24:14; Hebrews 11:13; (b) "to confess by way of admitting oneself guilty of what one is accused of, the result of inward conviction," 1—John 1:9; (c) "to declare openly by way of speaking out freely, such confession being the effect of deep conviction of facts," Matthew 7:23; 10:32 (twice) and Luke 12:8 (see next par.); John 9:22; 12:42; Acts 23:8; Romans 10:9,10 ("confession is made"); 1—Timothy 6:12 (RV); Titus 1:16; 1—John 2:23; 4:2,15; 2—John 1:7 (in John's Epistle it is the necessary antithesis to Gnostic doceticism); Revelation 3:5 , in the best mss. (some have No. 2 here); (d) "to confess by way of celebrating with praise," Hebrews 13:15; (e) "to promise," Matthew 14:7 .

Matthew 10:32Luke 12:8 PROFESSPROMISETHANK.
A — 2: ἐξομολογέω
(Strong's #1843 — Verb — exomologeo — ex-om-ol-og-eh'-o )

ek, "out," intensive, and No. 1, and accordingly stronger than No. 1, "to confess forth," i.e., "freely, openly," is used (a) "of a public acknowledgment or confession of sins," Matthew 3:6; Mark 1:5; Acts 19:18; James 5:16; (b) "to profess or acknowledge openly," Matthew 11:25 (translated "thank," but indicating the fuller idea); Philippians 2:11 (some mss. have it in Revelation 3:5 : see No. 1); (c) "to confess by way of celebrating, giving praise," Romans 14:11; 15:9 . In Luke 10:21 , it is translated "I thank," the true meaning being "I gladly acknowledge." In Luke 22:6 it signifies to consent (RV), for AV, "promised." See CONSENT , PROMISE , THANK.

B — 1: ὁμολογία
(Strong's #3671 — Noun Feminine — homologia — hom-ol-og-ee'-ah )

akin to A, No. 1, denotes "confession, by acknowledgment of the truth," 2—Corinthians 9:13; 1—Timothy 6:12,13; Hebrews 3:1; 4:14; 10:23 (AV, incorrectly, "profession," except in 1—Timothy 6:13 ).

CONTROVERSY.