Adsense is for putting ads on your site, and Adwords is for putting your ads on other sites (including Google search/shopping).
There's no "better", I think it really depends on a lot of factors; not least who is creating the ads? I'd rather use an expert at Google Adwords than a novice advertising on Facebook and vice versa.
That's a good point, Craig. I was a little confused about Adsense vs Adwords too, but an article by Digital Marketing Pro helped me a lot. Here's the link: https://www.digitalmarketingpro.net/adwords-vs-adsense-what-is-the-difference-and-can-i-use-both-on-...
It breaks the whole thing down with examples and relevant questions. Hopefully that helps you, webistorm!
Yup. Google Adsense is allowing Google to post ads on your website. If you're talking about Google Adwords vs Facebook ads - then Facebook ads are better for brand promotion and retargeting than lead generation. If you're looking to get new leads for your clients, then search engine ads are much better.