The reality is that there is a difference now, and it needs to be clarified. How would you, talking to another regular human being communicate to install an app that isn't in the official app store succinctly? If you just tell someone to 'install the app' then you are doing a bad job communicating. Economy of language means that new words are going to form to distill common concepts.

Package managers have existed for a long time, so the concept of app stores isn't new and is actually generally the accepted solution by the open source community. It's typically regarded as the safest way to install software as it comes with auditing and active management.

Side loading does a great job at communicating what is being done, and it helps consolidate the various ways you actually install applications into a nice generic term.

A store being locked down doesn't really have much to do with the concept of side loading anyway, since a locked down device doesn't support it in the first place.