Apache and Linux are often associated with the Internet; in fact both technologies have experienced their market penetration completely (Apache) or largely (Linux) due to the Internet. Both have similar roots, both sprouting from the open source (that is, non-commercial) software movement. And both have been propelled into the commercial marketplace due to support from huge commercial players. The big difference, however, is that Linux is an operating system, while Apache is a Web server. Often, Apache is deployed on Linux, and Linux is the "reference" platform for Apache. A reference platform is the first platform a product targets, and the majority of development and testing of the product takes place on that reference platform.
Actually, calling Apache a Web server is erroneous. Apache is actually an open (non-commercial) software group whose full name is the Apache Software Foundation. The Apache Software Foundation creates a non-profit forum for the development of software, and supplies hardware, infrastructure software, and other resources to support the open, collaborative development of software. Apache is a meritocracy, which in this case means in order to belong you must contribute. The most famous product to emerge from Apache is their Web server, but the Apache Web server has been ported to a variety of operating systems, not just Linux. The Apache Web server is by far the most widely used Web Server on the Internet, easily eclipsing Microsoft (number two) and Netscape/AOL/iPlanet (number three). The Apache Software Foundation also has other projects underway, such as for the open development of XML tools, and a Java-based application server.