Fain - Vine's Expository Dictionary of New Testament Words
Fain[ 1,,G1014, boulomai ]
to will deliberately, wish, desire, be minded," implying the deliberate exercise of volition (contrast No. 3), is translated "would fain" in Philemon 1:13 (in the best mss.). See DISPOSED.
[ 2,,G1937, epithumeo ]
"to set one's heart upon, desire," is translated "would fain" in Luke 15:16, of the Prodigal Son. See DESIRE.
[ 3,,G2309, thelo ]
"to wish, to design to do anything," expresses the impulse of the will rather than the intention (See No. 1); the RV translates it "would fain" in Luke 13:31, of Herod's desire to kill Christ, AV, "will (kill);" in 1 Thessalonians 2:18, of the desire of the missionaries to return to the church in Thessalonica. See DISPOSED.
Note: In Acts 26:28, in Agrippa's statement to Paul, the RV rendering is "with but little persuasion thou wouldest fain make me a Christian." The lit. rendering is "with (or in) little (labor or time) thou art persuading me so as to make (me) a Christian." There is no verb for "wouldest" in the original, but it brings out the sense.