I've had the play store install, remove, and modify installed applications without so much as a hint they were doing it, the "Play Store" does what would be considered "sideloading" applications (i. e. a third party app managing your applications from a location other than the package manager), feeding an apk to a package manager would just be "installing" an application like it always has been.

By co-opting the term to be something bad, they are trying to make it seem like they are the only safe source for applications (even though the Google-managed stores have just as much malware as WinMX did 20+ years ago).