The default arguments for get_posts() function include 'numberposts' => 5.
So if you’re querying for a search term that returns more than five (5) results the second query will return a maximum value of 5 unless you pass 's=computer&numberposts=-1' as your query string.
The WP_Query object doesn’t have a 'numberposts' default, although it is affected by the “Blog pages show at most” count in your settings panel. So if you want the total count using the query() function, you should override the defaults like this:
$search_query->query('s=computer&nopaging=true')