A prize is something that you work for and earn where a gift is something that you freely accept without merit.
Prize (brabeion) - the prize awarded to a victor, the reward (recognition) that follows triumph.
Strong's Concordance
brabeion: a prize
Original Word: βραβεῖον, ου, τό
Part of Speech: Noun, Neuter
Transliteration: brabeion
Phonetic Spelling: (brab-i'-on)
Definition: a prize
Usage: a prize.
Romans 6:23 - For the wages of sin is death, but the gift of God is eternal life through Jesus Christ our Lord.
Strong's Concordance
charisma: a gift of grace, a free gift
Original Word: χάρισμα, ατος, τό
Part of Speech: Noun, Neuter
Transliteration: charisma
Phonetic Spelling: (khar'-is-mah)
Definition: a gift of grace, a free gift
Usage: a gift of grace, an undeserved favor.