Those are both loaded and highly misleading terms, Fuerther, because they've been bandied around for centuries by people who failed to take the necessary time to learn how language is actually used.
What's proper for casual conversation is not proper for formal speech or writing, BUT the situation is the same reversed. Using formal language in casual conversation is "improper" because it's not appropriate.
The most accurate is; "I want to learn English appropriate to the social situation/register".