What is the practical difference between “ignorant” and “naïve”?
There is good discussion of the semantic differences in other answers, but the most important practical difference is that ignorant is a very insulting word that you should be careful about using, whereas naïve is not such.
In general naïve makes me picture a hopeful child who has unrealistic dreams and has not thought about the real world enough, whereas ignorant makes me picture a dumb, racist old man who won’t change his worldview in the face of overwhelming evidence.
So, for instance:
“I think you are being naïve, because...” is appropriate way to disagree with someone's theory at, say, a business meeting. It’s still a strong thing to say, and possibly condescending or belittling of your colleague’s theory.
On the other hand, “I think you are being ignorant, because...” is quite rude and aggressive. It's not practically very different from saying stupid even though the semantics differ.
"naive" (often naïve when just the adjective) emphasizes the immaturity of the person in that state. It implies that they lack experience that would make them aware. In other words, the expectation is that they are capable of knowing but do not yet.
She's naive, so she does not know he's toying with her.
"ignorant" implies an incapacity to know such that you don't expect them to learn.
He's so ignorant. That's why he doesn't understand French people.