So, what is the difference between a publisher and a distributor?

I thought they are the same. I assume you don't need to make a demo. You can just make a completed song, upload to a distributor, it will be published on all platforms, done.

Also, is Songtradr anything special? Is it better than other mainstream distributors such as CD Baby, DistroKid, TuneCore, etc?

A Canadian music producer, singer songwriter, composer, and professional guitarist.