The basic difference is that starter soil is essentially sterile to prevent seedling damp-off and potting soil has some fertilizers in it (synthetic or organic). I try to stay organic because I understand the contents better, but I have been known to add some dilute synthetic stuff when I'm out of the "good stuff". That small amount doesn't ruin my season.

I'm organic out in the garden, but a little synthetic stuff on the seedlings isn't meaningful.

My organic thinking is more about runoff, and a few drops of the "bad stuff" in a liter of water at the seedling trays isn't going to cause that problem.