Are these words used interchangeably in Linux?
Note: This answer is restricted to Ubuntu/Debian.
In general, no, they do not mean the same. A "package" is like an installer; it's a DEB file, much like MSI files in Windows.
Unless the application is relatively small, it will usually be assembled from multiple packages, with each package containing one (sometimes more) components of the program. These components can be binaries (executables), libraries, help files (man pages) and even source code.
Conversely, some packages will install multiple small programs (binaries), and others will "collect" multiple related programs under one umbrella for ease of installation (meta-packages), but these are the exception rather than the rule.
In short: since most programs are made up from more than one package, they are not the same. :-)
Software is a collection of Programs.
When that Software is used for performing a particular task , we say its an Application.
Now relating these terms for Linux- Ubuntu specifications.
Package is a specific piece of software which the system can install and uninstall.
Restricting to Ubuntu/Debian.
Packages are basically of two types : Binary packages and Source packages .
Since they require more developer friendly knowledge due to compilation and dependency technicalities , .deb was developed to provide simple installation and un-installation functions compared to Window MSI or .exe formats.
(.deb)ian package,is used by Debian and Ubuntu.
dpkg (lower level) and apt(higher level) forms its Package Management system (PMS) used to install them.
.deb package contains meta-information such as a package description, version, and dependencies which allows PMS , to perform an automatic upgrade to a newer version, to check that all dependencies of a package are fulfilled and/or to fulfill them automatically.
For example : sudo apt-get install ubuntu-desktop.
Where Ubuntu-desktop is a meta-package use to install the basic desktop applications required by the default desktop using apt PMS .
In the perspective of Ubuntu and Debian.
No, they are not the same thing. Package usually refers to the individual components of a full featured software. Where Software/Application/Program usually refers to a full featured software which can be used standalone.
Let's take an example:
Then default file browser in Ubuntu (unity) is Nautilus. We usually refer to this as "Software" or "Application", since they can be used for a specific needs i.e browsing files.
But this Nautilus Application or Software depends on various small components, which usually do not provide a full feature individually, but they can be used together to build up a Software, which can provide full feature (browsing files/folder) individually.
you can see what packages
nautilus depends on, by running this command in a terminal :
apt-cache depends nautilus
Hope this will help