According to an article on comicbook.com, the current Vixen is the granddaughter of the Legends Vixen.
Out of universe, the actress who played Mari McCabe was unavailable for filming Legends, so they had to cast a different actress. In-universe, the totem is a family heirloom, passed from mother to daughter. According to the official character description from CW and WB:
Amaya Jiwe – better known as Vixen – is the newest superhero to board the Waverider and join the ranks of the Legends of Tomorrow. Like her granddaughter, Mari McCabe, Amaya’s powers are derived from the mysterious Tantu Totem, which allows her to magically access the abilities of animals.
Note that the Totem was not found during Mari's lifetime. We know from Vixen that her older sister was the previous guardian of the Totem, who tells her of it's origins:
KUASA: Our people asked the god Anansi to protect them. He's known as "The Trickster," able to take any shape he wishes to combat his enemies. In exchange for our worship, he gave us a totem to channel his power. A gift to be passed from generation to generation. I was but four when I was chosen.
KUASA: Our mother left, with two things the most precious... the totem... and you.
Since Kuasa looks to be more than 4 years older than Mari, she inherited the totem before Mari was born, and from the previous guardian. That other person was probably Mari/Kuasa's mother. If we assume that all girls are "chosen" at the same age, then Mari's mother probably did not inherit directly from Amaya, since there's a huge gap in years and it seems unlikely that Amaya would go another 20+ years before having her very first child. It seems more likely that Amaya had more than one daughter, and Mari's mother inherited sometime in the late 60s and then passed on to her daughter in the late 80s.
On a side note: the character of Amaya Jiwe was created for the Arrowverse; she doesn't appear in the DC comics. However, Vixen's full name in the current DC continuity is Mari Jiwe McCabe, so this new character is an homage to the comics character.