The one on the left is her normal style.
Information:
Full Name: Princess Celestia or Queen Celestia
Nicknames: Celie, Tia, Mama, Mummy, Mum, Cay-Cay
Gender: Female
Age: Over 1111
Species: Pony (Alicorn)
Husband: Mirror King Sombra
Children: Princess Dark Sun (Daughter), Princess Skyline Shadow (Daughter), Prince Shadowing Sun (Son)
Place Of Residence: Castle of the Two Sisters (Formerly), Silver Shoals (Formerly), Canterlot
Personality: Gentle, Sweet, Kind
Parents: Queen Galaxia (Mum), King Cosmos (Dad)
Cutie Mark: Sun
Occupation: Ruler Of Equestria (Formerly)
Bio:
When Celestia was a young filly, she always wanted to be a princess and when she was older, her dreams finally came true and Celestia was crowned 'Princess Of Equestria.'
A few years later, Starswirl and 5 other unicorns lost their powers to raise the sun and moon so Celestia and Luna had to step up and do it instead and then they successfully got their Cutie Marks.
About 111 years later, Celestia had to banish her own sister to the Moon for 1000 years for refusing to lower the moon to make way for the dawn. After 1000 years, Celestia reunited with her sister thanks to Twilight and her friends.
About 9 years later, Celestia retired and gave Twilight the job of being Ruler Of Equestria. During her time in Retirement, Celestia met with King Sombra from the Mirror world again and they got married together and they both had their first child, Princess Dark Sun.
1-2 years later, they had their second child, Princess Skyline Shadow and 4 years later they have their third and final child, Prince Shadowing Sun.
When Twilight had her first child, Celestia visited Canterlot to congratulate her. But when Twilight had her second child, Celestia was too busy to visit but she sent Twilight a letter instead.
When Twilight got assassinated when her children were teenagers, Celestia was deeply saddened by the news and had to take her place back of being Ruler Of Equestria until it was a good enough time for her oldest child to rule instead.
Celestia still lives in Canterlot after Princess Dark Sun rules the Kingdom and whenever there is a special occasion, Celestia will put her mane in a different style (The one on the right.)