Is this a trick question?

The name 'Katherine' comes from the Greek 'Katharos' which means pure. It has been a popular name since the Dark Ages and was used by many European royal families. Catherine is a French form of Katherine and is also common in English.

Spelling, origin, there's also Katrina or Katerina as another version of that name.

One begins with a "C", one begins with a "K".

It's just a different spelling