The primary difference is that the search engine uses a complex set of algorithms to figure out a set of results that best match a set of keywords. Title and tags affect the relevance score more than the body content, for example. We go even further than this, leveraging social signals, such as activity and connections, modification date, and even "official" or "outdated" content to raise or lower the relevance score to put the best possible content in front of the end user.
The browse system, on the other hand, is a completely separate engine that queries content from the database, rather than the search index. It's more appropriate for browsing / exploring content when you aren't searching for a specific term. A good example is "Documents you've authored in the last week" or "Open questions in a group". You don't really care about a particular term, but rather the set of results that match your criteria. One of those criteria happens to be "filter by text" which doesn't change the way content is sorted to show the most relevant results, but simply removes content that doesn't have any matching terms. This filter is meant to enable me to still see a list of content I've created sorted by most recent first, but to be able to filter those results to only include content that contains the term "jive".
I agree that the filter by term box on browse can often be confused with search. As we move more signals into the search index, such as content your participated in, we'll be able to eventually merge these two experiences into one. Hopefully that information and context above will enable you to explain the difference to any end user that might ask.
Thanks Nick. Excellent explanation. You've earned a free beer at JiveWorld. Come by Akira's booth to collect.