In short, Your understanding is correct. Package managers only update those applications that
- come as a debian package,
- have a repository configured and
- the repository is still alive or active.
By package managers I'm referring to
aptitude, Synaptic package manager, Software Center etc.
To specifically answer your question -
- Build from source and install
Update requires re-building from source and reinstalling the application. Debian package managers have no knowledge of these applications. They don't get update by them.
There are debian-source packages that can be fetched from repositories through package managers like
apt-get source and compiled to debian package. These are fetched and then built to produce a .deb file. Then those debian packages can be installed. They will get update if fulfilled the condition for a manually installed .deb file.
- Install a binary
I'm assuming, by this, you are referring to just copying some binary programs in your system to use. Like how
rclone application is installed. Package managers have no knowledge of these applications and can't be updated using them.
- Install a deb file.
The conditions from the short answer apply here. If you install a deb file manually for which a repository is configured, these package can be updated through package managers. For example, if you had an already downloaded google-chrome .deb file and you installed it manually using
dpkg and you have google chrome repository configured, then this package will get update, provided that other conditions are satisfied.
- Install from repository
This is very obvious. If the repository is alive these will get updates from package managers.
If you remove all repository sources, package managers would be unable to even update most core packages!
apt-get manual page for details.