I just came across this video that demonstrates how most people don't know the difference between a browser and a search engine. They are confused between the two, and unable to define them:

So, for clarification, here is the difference, in layman's terms:

A Web Browser is an application (a program) that is installed on your computer. Think of it as a window to the World Wide Web. It provides a text box where you can enter an address of a web page--otherwise known as a URL--(http://www.somepage.com) and it interprets the code that the page is written in so that you can view it. Some web browsers are Safari, Internet Explorer, Firefox, and Chrome. Like a TV, a web browser is for viewing content. It doesn't produce the content (although it can store the files that you view in memory).

A Search Engine is a tool which gives you the capability you to search some collection of content. Your computer probably has a search engine built in so that you can search the files on it. Some companies have built search engines to search the World Wide Web for free, supported by advertising. So you can open up your web browser, and go to the web page of the company that has the search engine you want to use (www.google.com, www.bing.com, etc.). Then you enter your search terms and the search engine provides you links to web pages that match your search. Examples of search engines are Google, Yahoo, Ask, or Bing. (See my post on searching with Google for more information on search tips).