I would say usually when talk about going somewhere, or just generally talking about changing from one state to another. For example: "She walked into the store." This sentence would mean that a girl started outside of the store and then went inside, or into, the store. But "She walked through the store" would mean that the girl was already inside the store. Another example would be "He has turned into a really nice guy," meaning that the man was not nice before, but over time he has become nicer. Any questions? [emoji]

I read that "into" is usually connected with movement words.