There is a lot of interesting theories on this. Some say it's all nonsense, and others are very vocal zealots.

I'm not sure what the point of your question is as there are many ways to look at it.

Are you asking if they're the same? Different? People's perspectives?

No matter the question you won't find a definite answer here. What you'll get is opinions and maybe a few suggestions on where to go to get more info. Not being an expert, I'll just suggest you start by doing a Google search on the topics and plan on sifting through a bunch of BS and flaming debates to get to the useful information.

Chakra and chi are not the same. Chakra is based on Indian Philosophy and Chi on Chinese. Let me try and explain each of them separately:

Chakra: Based on Indian Philosophy there is a Kundalini energy, that flows through the chakras. This energy is called prana ( or life as in Sanskrit). There are seven chakras in human body and the energy travels through the seven chakras. Blockage of any of the chakra causes the blockage of the flow of prana and thus causes disease. It is believed that if you cleanse or clear your chakras you will get the ultimate health. The list of the seven chakras are as follows:

1) Muladhara chakra (base chakra)

2) Swadistana chakra (sacral chakra)

3)Manipura chakra (solar plexus chakra)

4) Anahata chakra (heart chakra)

5) Vishhudha chakra (throat chakra)

6) Agya chakra (brow chakra)

7) Sahasra chakra (crown chakra)

I have provided a picture with this answer of chakra ( Please note this picture is from Google and I have no copyright. It is just for your reference).

Chakra cannot be directly associated with martial arts. However some link it with traditional martial arts like Kalaripayyatu. It is of yogic origin and used for meditations.

CHI: Chi is the life energy. Unlike chakra it is not points present in the body, but the life itself. Chi flows through the body. Concentrating chi on a certain part of body makes it strong. It is based on Chinese philosophy. The same is called Ki in Japanese. Chi can be associated with Chinese martial arts. Tai chi being one of it that concentrate on chi manipulation.

Please note that some consider it as fake and just myth. It is upon you to believe or not. Hope I cleared you doubt.