It’s a practice that’s fairly common to APT, Yum, etc. It’s there to differentiate between “the version of the software being packaged” and “the iterations/version of the packaging approach itself”. For example, if the build pipeline has changed, or a previous iteration accidentally included something it shouldn’t or omitted something it should, the version of the software being packaged hasn’t changed but the artifact itself will be different. It’s useful to be able to indicate which specific historical contents you have, in shorthand, without relying directly on checksums or another content-addressable approach.

If you’re building the release locally, your server doesn’t need Distillery or even Elixir FYI.

Based on the output of elixir --version it appears that you aren’t actually using 1.7

You can also choose the OTP major version when you install elixir via asdf.

asdf install elixir 1.7.x-otp-20

This will install elixir 1.7.x but compiled with OTP 20.

Why? Is there a specific dreason?

This massively depends on your operating system.

Just asdf should be enough. Follow the installation instructions, then

asdf plugin-add elixir
asdf install elixir 1.6.5

should do the trick. Usually I also add the Erlang plugin and manage OTP the same way (and an even dozen other languages as well, all stashed in my ~/.tool-versions so that a single cd ~; asdf install will sync a new machine with the languages and versions I use at any given time).