今天 = 今日 = today. Using 日 is more formal, poetic and a preference in use in southern China. Like in all languages, using the formal word conveys your tone, emphasis and mood of the moment. So therefore those saying that it is archaic is utterly nonsense. However, 天 (sky, heaven) and 日 (sun) are not interchangeable. 日落 = sunset, 天落 = something fell from the sky. 天子 = son of heaven = emperor is definitely not the same as 日子 = "days".
这天 = this day, NOT that day or someday. "Someday" = 有一天.