GSC: Why does GSC show more links than other platforms?

All tools are different and will show different results. Google Search Console is likely the MOST accurate – after that, I’d recommend Ahrefs as the next best link based SEO tool. A recent student put this question to Moz – and received this reply from them which I thought was worth sharing:
“Mozscape index, which powers Open Site Explorer, is still growing, and while it is large, our index doesn’t cover the entire web. You can always check our update schedule at any time, as well. Most new sites and links will be indexed by our spiders and available in Mozscape and Open Site Explorer within 60 days, but some take even longer for a variety of reasons, including the crawl-ability of sites, the amount and quality of inbound links to them, and the depth of pages in subdirectories. The index is based on a breadth-first approach, starting at the top of a site’s hierarchy and moving down from there. You might want to check to see if we have indexed the pages linking to your site. You’ll also want to make sure that we aren’t blocked from crawling the site. If our web crawlers are blocked from crawling certain pages (i.e., with “noindex” or Robots.txt), they may not be included in the index. Finally, the best thing you can do to help your domain become indexed in OSE is to work on building links from sites with high Mozrank. You can learn more about link building in our handy guide! Generally, we recommend using a wide variety of backlink tools to get the most illustrative picture of how your site’s backlink profile looks. OSE and Ahrefs index differently and have different purposes. Ahrefs is good for quantity while OSE is great for finding higher quality links. Domain Authority is our own proprietary metric that is closely correlated to Google rankings, so our customers often use OSE to research influential sites to build links.”