Great, question. Same company (Google), two massively different platforms.
Google Search Console is a reporting and diagnostics tool for SEO, search engine optimization. If you’re looking to get your site to rank on Google organic search for free traffic, this will be a very useful tool to use.
Google Adwords (aka Google Ads), is a platform for buying traffic. Through Google Ads you can pay for sponsored ads, targeted against specific search keywords. Unlike SEO, this is where you pay for traffic. Google typically charges for every click. On Google Ads you can also advertise display banner ads, have app campaigns, and advertise on YouTube.