两种说法都是对的。人们最先使用的是 Web site，后来随着互联网的发展，Web site越来越普通，甚至成为人们生活中的一个组成部分，所以Web site也就演变成了一个普通词汇，即 website。下面是《美国英语传统词典》的相关解释：

The transition from World Wide Web site to Web site to website seems to have progressed as rapidly as the technology itself. The development of website as a single uncapitalized word mirrors the development of other technological expressions which have tended to evolve into unhyphenated forms as they become more familiar. Thus email has recently been gaining ground over the forms E-mail and e-mail, especially in texts that are more technologically oriented. Similarly, there has been an increasing preference for closed forms like homepage, online, and printout.

翻译：从使用World Wide Web（万维网） 一词到 Web site（网络网站） 一词，再到 website（网站） 一词，其渐进过程，似乎就像网络科技本身那样进步快速。当 website 发展成为一个小写单词时，也正反映出其它科技字眼的发展也趋向于成为一般无连字符号单词，而且越来越为人所熟知。所以，email 一字近来已逐渐普遍取代 E-mail 及 e-mail，尤其是在比较科技类范围的文章中。同样的，也有越来越喜欢采用封闭形态字型的趋势，例如 homepage（首页）、online（在线）和 printout（印出）。