Healed vs cured

Acts 28:

8 It happened that the father of Publius lay sick with fever and dysentery. And Paul visited him and prayed, and putting his hands on him, healed him.

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Paul healed him miraculously.

Strong's Greek 2390, 27 Occurrences

BDAG ἰάομαι: ② to deliver from a variety of ills or conditions that lie beyond physical maladies, restore, heal.

9 And when this had taken place, the rest of the people on the island who had diseases also came and were cured.

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Strong's Greek: 2323. θεραπεύω (therapeuó) — 43 Occurrences

BDAG θεραπεύω: ② heal, restore
in the var. senses of ‘care for, wait upon, treat medically
On medical practice in the Gr-Rom. world, s. ANRW II/37/1–3, ’93–96. B. 306. DELG s.v. θεράπων. M-M. EDNT. TRE XIV 763–68. TW.

The meanings of G2390-healed and G2323-cured overlapped. However, G2390-healed was often used in a supernatural sense, while G2323-cured was often used in the medical sense. Luke was with Paul on this occasion. He was a physician. He might have participated in offering his medical expertise in verse 9.

10 They also honored us greatly, and when we were about to sail, they put on board whatever we needed.

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In the end, they honored Paul and Luke.

The words heal and cure in English also carry these respective nuances.