In the 'olden days' of blogs, as I am sure some people remember, changes to the blog were made directly on the template. This practice can still be seen in certain circumstances, for certain reasons - BUT - Blogger has changed with the advent of New Blogger, and now New Designer Templates, and so have the reasons, and ways, for 'tweaking' your blog.
I'm sure a lot of the confusion, in many cases, stems from the persistence of Blogger, in maintaining reference to the 'old Classic template', or the even newer 'Layout template' in help guides, and the 'newbies', or new bloggers, are not sufficiently knowledgeable with Blogger, to know. Hopefully, in my humble opinion, one day (soon), all the old-style blogs will be memories, but until then, we have to try to help bloggers sort things out. I would, however, be investigating upgrading my blog(s) if I was using the older style templates. Things are going to change, and possibly very soon, I'd imagine, though, like with most things, there'll be support - for a while! I see no urgency about this, just convenience.
Recently, a blogger was trying to find where, in the blog html (template), to add script for a gadget. In the 'olden days', the script may well have been added to this, or that section of the template, but not any more.
For adding gadgets, eg: counters, or buttons etc, my general rule of thumb is: -
Similarly, if you want to make changes to the CSS (Cascading Style Sheets)- add it via the Design screen - Template Designer - Advanced - Add CSS feature.