A lot of people confuse the goddess Kali with Kali-Yuga. The main reason is that Sanskrit does not present itself exactly in roman alphabets, without diacritical markings. The goddess “Kali” is k-(long) a-l-(long) i. The age “Kali” is k-a-l-i. The difference is that in the goddess the a and i are long and in the age the a and i are short. In sanskrit a long a is as different from a short a as t is different from b or d in English. They are entirely different letters. It would be better to spell it:
Age of Kali
Kali (as in the age) means “one.” So kali-yuga just means “Age One.” It’s called Age One because it only has one fourth power. The word “kali” specifically means “the side of a dice marked with a 1.” So, the word also implies “worst” or “lowest.”
There is a divinity named kali, but it is not the goddess kaalii. It’s a male deity who is the son of Krodha (anger) and Himsa (violence). His sister is Durukti (harshness), and he impregnates her to have the children Bhaya (fear) and Mrtyu (death).
So Age One is the worst one, and these sorts of traits come out into the world very abundantly.
Goddess Kaalii is entirely different. She is the divine energy in a destructive form. As such she is a destructive mood of Shiva’s consort, Parvati.