Local SEO targets local search specifically. Which means that your audience is within a few miles from your business location and that your online presence is meant to drive foot traffic to an actual establishment. This is done through several methods including using geo-centric keywords, producing locally relevant content, building citations on local niches and directories, etc.
National SEO is location neutral. It's ideal for websites that generate revenue exclusively online or are just looking to generate awareness through a wide audience. If you're running a nationwide campaign or an e-commerce campaign, this is the perfect methodology for you.