The word ἐργάζομαι (from ἔργον work ') is 'to work,' and supposes activity of service as connected with life, natural or spiritual: thus the Thessalonians were exhorted to work with their own hands for a livelihood. 1 Thess. 4:11. See also Gal. 6:10, where there is positive labor expended in doing good to all.
ποιέω ‘to do, practice,' has more the character of conduct. In several passages both words occur. "He that doeth (πο.) truth cometh to the light, that his deeds may be made manifest, that they are wrought (ἐρ.) in God." John 3:21. The Jews sought to slay the Lord "because he had done (πο.) these things on the Sabbath day. But Jesus answered them, My Father worketh (ἐρ.) hitherto, and I work (ἐρ)" Chap. 5:16, 17. "Then said they unto him, What shall we do (πο.) that we might work (ἐρ.) the works (ἔργα) of God?" Chap. 6:28. "Whatsoever ye do (πο.), labor (ἐρ.) at it heartily, as to the Lord, and not unto men." Col. 3:23. "Beloved, thou doest (πο.) faithfully whatsoever thou mayest have wrought (ἐρ.) to the brethren, and those strangers." 3 John 1:5