Firstly notice you do not get the offer to install a clean shortcut in all websites.
Here are two example with default Browser. Using our own forum site, the space in the “share” section where I expect to see "Save to home " is replaced by “Install app”. The same happens with many websites !
In the second example is a site where we see “Add to Home screen” resulting in what I understand to be a pure shortcut, where the shortcut will simply open the url in the Browser.
Update, interesting, doctolib.fr seemed very keen to have me install the app; but at a second attempt a url shortcut was added finally ! Of course not all organisations do offer full functionality by HTML !