These two words have the same meaning and it is energy. Chi is the Japanese form while Prana is the Indian. Let's understand the difference:
Chi: The life force energy, which comes from the origin of traditional Chinese medicine. Chi moves through the meridians and also the three dan tiens, which acts as the gateways to pass through. These are one in the pelvic region, heart centre, and one at the third eye centre.
Prana: This is also a life force energy, but has come from a different tradition that is yoga and Ayurveda. It usually moves through the energetic pathways, which is also known as nadis. Like Chi, Prana is also associated with seven chakras which are unique to the yoga tradition.
These two forms, Chi and Prana are very similar in nature. Though the origin of two is different and ancient healing traditions, so they are slightly different from one another. The Chinese medicine mind and Ayurvedic mind views are different and reserved their importance differently.
Well, at last, if these two force energies are balanced and flow well, a person would be healthy but when it alters, it causes diseases. So, in other sense as well, they are quite similar.