Idiot’s Explanation-Guide To Tag vs Categories?

Okay, please forgive what a huge idiot I am for asking a question like this…but can someone explain to me what the heck the difference is between “tags” and categories” and what-the-heck-on-earth purpose they serve?

I’ve been trying to use these on my new site https://www.theadjunct.net, but they seem to inter-twine with one another and mess things up. If anyone can dumb-it-down-a-little for a new blogger like me, then I would be ever so grateful!

Thanks, as always, in advance.