There are two types of invitations: formal and informal. Formal invitations use polite language like "I would like to invite you to" or "Would you like to" along with accepting responses like "Yes, I would love to" or refusing responses involving apologies. Informal invitations are more casual, using language like "Will you come" or "Why don't you" paired with shorter accepting responses like "All right just a quick one" or refusing responses including thanks and an excuse.