In a horse stance (kiba dachi) the feet point straight ahead, vs in shiko dachi (four point stance) the feet are turned out.
The differences in stances will have an impact on balance and centre.
In various IP/IS exercises, you could stand in shizentai, or in a wide version of shizentai -- i.e. with the feet most likely somewhere between parallel and angled out at 45 degrees. Since many of the exercises cycle between the states of back open / front closed and vice versa, you alternatingly get the qualities of both stances, but it is the center that drives the feet vs. the placement of the feet that dictates balance and center (to Dan's point).