Scott,
You've got the gist of it. Over ten thousand DNA projects exist at FamilyTreeDNA.com, most with Y-DNA kits, and many with autosomal DNA. The results from Y-DNA tests can show family connections going back hundreds of years, but only on the all-male line. In contrast, autosomal DNA tests (Ancestry, 23andMe, LivingDNA, MyHeritage, etc.) can only turn up connections in the past maybe 5 generations or so, but can find connections on all of your ancestral lines.
FTDNA provides a few resources for surname projects, but quite a few used to depend on some sites that shut down after the arrival of the European General Data Protection Requirements (GDPR), and many now only have skimpy sites at FTDNA. The idea here is that WikiTree could fill the need, providing a home for additional information that doesn't fit at FTDNA, also allow folks who have tested through other companies to connect, and provide some additional features.
It's still "early days" for support of surname DNA projects at WikiTree. If you're not the admin of a surname project at FTDNA, you could possibly start organizing one here at WikiTree, but otherwise you definitely could make sure that your tree here is correct, and add information to indicate the DNA tests you have taken.
FYI: Here's the Horn/Horne project at FTDNA:
https://www.familytreedna.com/groups/horn/about
Two more notes: You can download your raw DNA from many of the existng companies (Ancestry, 23andMe, MyHeritage, LivingDNA, etc) upload them to FamilyTreeDNA.com, join one or more projects, and look for matches, all for free. If you wish to get FTDNA's estimate of your ethnicity, or use their chromosome browser to review matches in detail, you'll have to pay a modest one-time fee ($19?). You'll find similar deals at MyHeritage.com, LivingDNA.com, GEDmatch,com, Geneanet.org, and a few other sites. Each has their own privacy policy and listing of terms and conditions.