Businesspeople may say to a client, “Good morning, Mr. Jones. How are you today?” The same businesspeople may say to a college classmate, “Hi, Jack. How’s it going?” The point here is that even Americans use a kind of keigo depending on the person they are talking with.
In general, polite language is longer, more clearly enunciated, and uses no reductions. By contrast, informal language (not slang) omits unnecessary words, reduces words and often ignores grammatical rules. It is true that English does not have the same kind of “polite set phrases” that Japanese does, but that does not mean Americans speak to everyone in the same way in every situation.
In a formal invitation, a person may say, “I would like to invite you to go with me to a concert.” By reducing “I would” to “I’d” and eliminating “with me” the same person makes the invitation, “I’d like to invite you to go to a concert.” There is a perceptible change in the formality, but the second invitation is no less polite. It is simply less formal and more friendly. If we continue to make the invitation shorter, it becomes “Want to go to a concert?” And in the ultimate reduction, “Wanna go to a concert?” This last form is used by close friends, especially young people.
While American manners require language that is polite, it is not always necessary to be formal. As in most things, taking the middle ground is the safest way, such as in the second invitation above.