Those two words spring from the same Latin root. However, sharing the same historic root does not guarantee their meanings to be similar today. Here are just a few examples of this phenomenon: "incredible" and "credible" "liberal" and "liberty" "vision" and "revise" "stationary" and "stationery" "fact" and "factory"

ignorance = state of ignoring it does have the same root meaning if you want to describe someone who is ignores, you can call them ignorant or an ignoramus

The word comes from French. In that language, both meanings are retained. Although ‘ignore’ and ‘ignorant’ are both common words, it’s always good for English learners to think about how to say things by stringing together short words of Germanic origin.These are the words first learned by native English speakers when they are toddlers. I don’t know./I don’t know anything. I don’t care. /I don’t care about it.

There's an element of agency or intentionality that shades the meaning of ‘ignore’ from ‘ignorance,’ but they both involve a lack of information or awareness. The verb version describes the process by which a person remains intentionally ignorant (by ignoring something), whereas ‘ignorant’ is the resulting state that results from the process/action of ‘ignoring.’ ‘To ignore’ is to intentionally avoid learning, considering, or paying attention to some kind of information. Psychologically, you could argue that ignoring something could be subconscious rather than willful or intentional, but that's a more complex question. 'To dismiss' something is a related concept, but it implies that the person thinks that the thing to be ignored/dismissed is insignificant or otherwise inconvenient to consider. ‘Ignorance’ is to lack information or knowledge about a particular subject or situation–there can be both intentional ignorance or unintentional ignorance. A person achieves ignorance by ignoring things or otherwise failing to achieve knowledge on a subject or situation. Realistically, we are all ignorant of 99.99% of things due to human limitations, and our limited ability to understand things, to pay attention to things, and because of our own cultural biases or environments that we live in. ‘Intentionally ignorant’ can be used to describe someone who is purposely ignoring something.