I wanted to add the Thymus serpyllum, was redirected to the Thymus praecox subsp. arcticus. There are a lot of cultivars in the Thymus serpyllum list, but mine is just the Thymus serpyllum and it doesn't look like the Thymus praecox subsp. arcticus. I'm confused

Nevertheless, T. serpyllum is no longer an accepted name. The plant has been reclassified, along with some other species, as T. praecox subsp. arcticus. I don't grow either of these, and we have no photos of them in the database, but I see no appreciable difference in the Google images of the two.

https://www.google.com/search?...

https://www.google.com/search?...

There is a lot to do about the naming of Thymus species. Here is a list with synonyms. The first is the synonym, the 2nd the 'real' names.
Here is Thymus serpyllum an accepted name and the Thymus praecox subsp. arcticus is renamed as T. polytrichus subsp. britannicus.
http://www.users.waitrose.com/...
http://www.users.waitrose.com/...

So confusing.
Is your information from a more recent date?

Yes. This is the most recent information:

http://www.catalogueoflife.org...