I wondered whether it might just be a nickname or a case of two different Chinese words translating to the same English word, but nope, both are 天网.

Here's the Baidu Baike page on Skynet from the movie: https://baike.baidu.com/item/%E5%A4%A9%E7%BD%91/3030631

Here's a post by the Chinese government, reporting that internet users demand Skynet to reach full coverage faster: http://www.gov.cn/zhuanti/2017-03/17/content_5178139.htm

So if it's a nickname, the Chinese government has no qualms about using it.