Winx/Fairy is the basic fairy level used in first, second and third seasons. On the Nickelodeon version, the term "Winx" is replaced by "Magic Charmix".
Charmix is an upgrade and power-up introduced in second season but dropped in the third seasons, and completely ignored by Nick when they did the specials.
Enchantix, introduced in third season, is the fairy power required to become a guardian fairy and graduate from Alfea. A fairy earns her Enchantix when she willingly sacrifices herself for someone from her home planet or someone she cares about, directly or indirectly.
Fairy dust is an incredibly powerful ability associated with Enchantix used to overcome all dark magic and spells.
Believix, introduced in fourth season, is a fairy power that is required for fulfilling greater purposes than just guarding the magic realm. Winx Club members earn their Believix when they attempt to bring magic back to Earth by making the people believe in fairies and magic. Believix also give the fairies additional wings that are specific in function.
Special Believix wings:
Speedix are wings that they use to enhance their speed in flying.
Zoomix are the wing that they use to teleport.
Tracix are the wings that they use to see the past.
Gifts of Destiny:
Sophix is a power-up of Believix granted by the Ethereal fairies, which the Winx Club use to face Diana, major fairy of nature, and her Amazon fairies.
Lovix is a power-up of Believix granted by the Ethereal fairies, which the Winx Club use to face Aurora, major fairy of the North, and her Arctic fairies.
The Black Gift is a power-up of Believix granted by the Ethereal fairies. It can return the dead to life, but can only be used once per person.
Sirenix is a mystical fairy power created by the infinite ocean itself. To acquire it, a fairy must complete a quest to find 3 gems for her Sirenix box with help of the Harmonix power, while being guided by the riddles from the book of Sirenix and with help from her Sirenix guardian. If they fail, their magical powers will be taken from them forever. However, the ancestral witches have placed a curse on it, which would result in the power turning over the fairy herself, leaving a soul without a body, like it did to Bloom's sister Daphne.
Harmonix is a fairy power granted by the book of Sirenix in the fifth season. More powerful than Believix when on land or air, it grants the fairies to swim and fight underwater better. This helps them in completing their quest for Sirenix. The Box of Sirenix gave them Harmonix powers (Note that Harmonix comes before Sirenix and not after). They gain Harmonix in season 5.