In America, that difference would mainly be reflected in tone of voice, and use of slang words. In Japanese however, there are actually different words and verb endings used. In many Japanese language courses, the polite form is taught first. The plain form is only acceptable with friends and close family members. However, you hear the plain form spoken all the time in Anime, video games, and Japanese TV shows.
Songs also use the plain form almost exclusively.
Many people complain that they still can't understand much Japanese even though they took a 2 year college course. That is because colleges often focus on the wrong subjects. Although both are useful, I have found that there are many things more useful to learn. There are people who strongly believe you should learn the polite form first, because it's easy to create the plain form from the polite form. The instructors who insist on prioritizing the polite form do have their reasons.