What's the difference between 周 and 星期?
Dividing a year into 52 weeks was a new concept to Chinese people at the time. Since 星期(指七夕，就是牛郎织女鹊桥相会之日) a common term already existed in China,
https://zh.wikipedia.org/wiki/%E6%98%9F%E6%9C%9F it was then used to express a &quot;week&quot;.

中國古代有七曜这一詞
*The Japanese still use 七曜 for the name of their days in a week - (日曜日, 月曜日, 火曜日 水曜日, 木曜日, 金曜日 and 土曜日)

Meanwhile, there was another common Chinese term 周天 (a circle of) http://baike.baidu.com/item/%E5%91%A8%E5%A4%A9/909115 therefore, 周 was also borrowed to describe  &quot;a week&quot;
As for practical usage,  周 and 星期 are interchangeable, but 周 is more formal and 星期 is more colloquial.
Also, the single syllable 周 doesn't take classifier, but 星期 does. We say 一星期 or 一個星期, but we only say 一周, not 一個周
both 周一 and 星期一 mean &quot;Monday&quot;, as mentioned before, and they are interchangeable, only 周一 is more formal and 星期一 is more colloquial