apt is a more recent tool, combining functionality of the older tools apt-get, apt-cache, etc., and is aimed to be more optimized for interactive use.
Both apt search and apt-cache search serve to retrieve package names that fulfill a search criterion.
apt-cache search by default lists package name and short description on a single name:
~$ apt-cache search xvile
vile - VI Like Emacs - vi work-alike
vile-common - VI Like Emacs - support files for vile/xvile
vile-filters - VI Like Emacs - highlighting filters for vile/xvile
xvile - VI Like Emacs - vi work-alike (X11)
apt also provides version information and architecture, in a two line format:
~$ apt search xvile
Sorting... Done
Full Text Search... Done
vile/jammy 9.8v-1build1 amd64
VI Like Emacs - vi work-alike
vile-common/jammy,jammy 9.8v-1build1 all
VI Like Emacs - support files for vile/xvile
vile-filters/jammy 9.8v-1build1 amd64
VI Like Emacs - highlighting filters for vile/xvile
xvile/jammy 9.8v-1build1 amd64
VI Like Emacs - vi work-alike (X11)
only searches package name and description. With the option provides a compact list of package name and description
With the --full option, apt-search provides full package info for all found packages:
~$ apt-cache search xvile --full
Package: vile
Architecture: amd64
Version: 9.8v-1build1
Priority: optional
Section: universe/editors
Origin: Ubuntu
Maintainer: Ubuntu Developers <ubuntu-devel-discuss@lists.ubuntu.com>
Original-Maintainer: Brendan O'Dea <bod@debian.org>
...information that with apt, can be retrieved with the show command for individual packages:
~$ apt show xvile
Package: xvile
Version: 9.8v-1build1
Priority: optional
Section: universe/editors
Source: vile
Origin: Ubuntu
Maintainer: Ubuntu Developers <ubuntu-devel-discuss@lists.ubuntu.com>
Original-Maintainer: Brendan O'Dea <bod@debian.org>
Bugs: https://bugs.launchpad.net/ubuntu/+filebug
Installed-Size: 1,509 kB
apt-cache search can be made to search package names only with the --names-only option:
~$ apt-cache search xvile --names-only
xvile - VI Like Emacs - vi work-alike (X11)
Which one to use?
In principle, apt is developed specifically to be your more simple day-to-day interactive tool, but ultimately the choice is yours. All of these APT tools will continue to be around.