Libraries and applications in the erlang world are one and the same. The notion of an application is used because while libraries are often thought of as just bundles of code, libraries in Erlang can also start stateful processes when loaded to manage the state of that library, and are thus better thought of as applications.
A good example would be the package Briefly, which generates temporary file paths. It has code / functions that let you ask for a temporary file path, but it also manages in memory process state to ensure that the paths are deleted when no longer in use.
As noted by @Ankhers, applications define a range of acceptable versions for each dependency ( ie ~> 1.0). When you to a mix deps.get for the first time mix will attempt to find a specific version for each application that falls within all the defined versions. If it cannot, you have the option to override the version to be whatever you want, and see if things work anyway.
Most of the time though it isn’t too hard to get a set of versions acceptable to all relevant libraries.
