The search box has many more features than the Ask Question title box. You can see the options here.. Also the search box strips away common words and keeps keywords. But outside of that they should be searching the same things.
Make sure when you're searching in the search box to use it like the ask question box. But remember that it is stripping away non keywords. You can even see what words it's stripping out.
Here I'm asking the question "When are the dev days happening?
When you click that and then click any tab (like relevance or newest). Then check out what the search query is consisted of. In this case it's changed to "dev days happening"