I know the definition of both of these words are Sunday but in what context are they used?
2 Answers
周日 is formal(on TV news) and oral, 星期天 is mostly oral. 星期日 is what Cantonese use orally(Hongkong, Canton), mandarin hardly.
We also use 礼拜天(mandarin)礼拜日(Cantonese) orally a lot.
Most possible combination of is above. btw There is no 周天.
As a native speaker in mainland China, I don't agree with that 星期日 is hardly used.
1 周 星期 礼拜
周 and 星期 are both more commonly used than 礼拜. It's hard to tell which one is more formal. It's only a matter of personal habits varying from ages and regions.
2 日 天 for Sunday
周天 and 周日 both mean Sunday. 周天 is informal.