A website (usually one word, though a few publishers use Web site or web site) is a collection of linked documents and content associated with a single organization, person, group, or topic and usually sharing a server and a domain name. A web page (usually two words) is a single page of content on a website. For example, this post about the difference between website and web page is a web page on the Grammarist website.
Mixing up the two is not a serious problem. It happens frequently, though it can give the impression that one is not up to speed on the parlance of today’s technology.
A decade ago, the two-word web site was far more common than website, and Web was conventionally capitalized (as was Internet). And though some inflexible publications hold to the old convention, English’s compounding impulse has done its work, and website is now about three times as common as the two-word varieties. Web site is particularly strong in American English, perhaps due to the influence of New York Times, whose editors insist on sticking with Web site. Outside the U.S., the two-word forms are much rarer, and web usually isn’t capitalized. Web page is still more common than webpage, but we can probably expect this to change soon enough.
Examples
The website set up for the resale of unwanted tickets sparked anger and confusion among members of the public after it crashed. [Financial Times]
Recently, the web page of one of his listings … was copied and listed by scammers as a rental. [Newsday]
According to figures from job-hunting website seek.co.nz, the average pay packet offered by employers rose by more than $3000. [New Zealand Herald]
Having the screen freeze routinely is a jarring experience, particularly when you’re just trying to scroll a Web page. [LiveMint]