All software downloaded from the repositories using Synaptic or Muon
goes into /var/cache/apt/archives/. There are quite a few command line
programmes and they do not appear on the menu. Generally "consumer
oriented" software like Office and Browser apps appear on the menus
but also many niche programmes.

If you can't find it on the menus it might appear after a reboot
(faint hope though!). You can find the names of all the files
installed for each app in Synaptic. Look for what is most likely to be
the main executable and type it in a terminal programme. If it was
really properly installed this will enable you to start it, although
you may have to try more than on name to find the main executable.

Not all applications in the repositories are graphical. Many are just
commandline or scripts and as such will not get a menu launcher. To use
them you have to open a terminal and type the command.

It is rare for a graphical aplication not to get a launcher in the menu,
but it can happen, especially if you use an outside sources or install from
a binary because these are not configured by the package maintainer. You
can edit the menu manually to add a launcher.

There are other reasons as well. If the application requires root
permission or if the application does not completely finish the
installation. A good way to test it is to open a terminal and launch it
with the command. It will usually give you error messages that would not
show otherwise, such as not configured, you need root access or not
installed. These error messages can be helpful in troubleshooting.

Also, some programs go into a surprising location. For example, the Adobe Reader
appears under Office applications, as does Calibre.

Yes and I have found a few even change names from what you might expect.
For example, gnome-tweak-tool may show up as Advanced Settings. I think
this is done to be more user friendly, but it is causing some confusion.