From apt-get documentation,
apt-cache search <search_term> will find packages that include
So if you want to get "software-center" to show up in the output of a
apt-cache search command, you should try
apt-cache search software-center.
Another related command can be
dpkg -l *<search_term>* which will find packages whose names contain
<search_term>. Similar to apt-cache search, but also shows whether a package is installed on your system by marking it with ii (installed) and un (not installed)
apt-cache search is a very rudimentary tool, basically implementing grep on package's descriptions. It often returns too many results or none at all when you include too many keywords.
axi-cache search <search_term>, on the other hand, provides better results, sorted by relevancy. It uses the Xapian search engine and is part of the
apt-xapian-index package which indexes all package information. It knows about tags and returns results in a matter of milliseconds.