"Installing" has the connotation of doing it directly from the Play Store. This is also known as "Downloading" (because the data is on a server, in the cloud, and you're fetching it "downstream" to a local device.)

"Sideloading" doesn't refer to the installation process, but to the file transfer process. You're sideloading when you transfer, e.g. APKs from your notebook to your Android. Or, from a USB stick into your phone or something.

In general, though, "sideloading" also refers to any "non-app-store" installation. It's a kind of colloquial shorthand. It's not really a technical term. But it's adequate for getting the point across.

If you just called it "installing" without qualifying it, how would anyone know that it's a different process, or that it's accomplished not by navigating to the app store? It seems that you would invite ambiguity here!