Make sure you have Search Console setup for the http://www.yourdomain.com also http://yourdomain.com, in addition to any other subdomains like https://www.yourdomain.com. You can also verify links with an additional backlink crawler. Remember you are looking at diverse indexes by diverse data sources, so you will see some disparity in results (diverse numbers and links for diverse backlink reports.)
To get an improved understanding around your backlink profile my commendation is to use a pair of tools (OSE, Majestic, aHrefs, etc) in addition to the data delivered in Search Console. Export the backlink information from all sources into Excel, de-dedupe the statistics (so you're not seeing at duplicate links) and review where the links are coming from. Using more than 1 tool will provide you a much better understanding what is out there, so see which ones work for you and your budget.
Also, ensure you have the precise version of your site in Search Console. Google will identify multiple disparities as diverse sites (HTTPS/WWW/HTTP/Non-WWW). You'll also want to set a favored domain (www vs. non-www) to aid Google in combining data.