My understanding of google analytics is that it is a 'free' tool which gives site operators bird's eye information on site traffic like the old fashion visitor counters all the way down to very granular information like what buttons users click on.

I have no idea what google tag service does. Based on a prior conversations I've had, I believe it has something to do with SEO.

If you don't know what I'm talking about, use the developer tools in Firefox to view the HTML of the page you are on. In the header you'll see javascript blocks. You'll see google analytics and tag service on just about every site, often meta or amazon, and some with completely unidentifiable names. I imagine the latter are the non big tech third parties we accept with cookies, but I'm not sure about that either.