Search feeds provide a powerful way to search outside of FeedDemon's subscriptions. To subscribe to a search feed, click the Subscribe toolbutton, then select "I want to create a keyword search feed" and click Next. Then choose a feed search engine and enter your keyword, and FeedDemon will subscribe to a dynamic feed containing the search results for that keyword. This is a great way to find out when someone is talking about a topic of interest in a feed you're not already subscribed to.
A watch searches within the feeds you're subscribed to in FeedDemon, whereas a search feed enables searching all feeds that are indexed by a specific search engine.