I’m not sure what you are trying to achieve with this variants. If you want to get the absolute URL to your homepage you might want to use:
<a href="{{ absURL "" }}">Home</a>
nevertheless your code produces the same output for me:
as a guess I would think these code l,ines are just copied from different places in your template(s) having other code around and the _CONTEXT-DOT at .Site is different.
Well, it’s 1) less room for errors (you get an error if you e.g. type site.Shome) 2) I think in general it’s a good practise to use the Page object for linking/navigation, which becomes more obvious in more complex examples.