I'm just trying to do this from the chrome console on Wikipedia. I'm placing my cursor in the search bar and then trying to do
document.activeElement.innerHTML += "some text"
value is normally used for input/form elements.
innerHTML is normally used for div, span, td and similar elements.
value applies only to objects that have the value attribute (normally, form controls).
innerHtml applies to every object that can contain
HTML (divs, spans, but many other and also form controls).
They are not equivalent or replaceable. Depends on what you are trying to achieve