None at all.

I use them interchangeably.

No, "dress" typically refers to women's clothing. For men's wear, use terms like "outfit," "attire," "suit," or "ensemble." Austintrim https://austintrim.co/

It's just a difference of dialect. In my region of America, we only say "clothing store." The term "clothes store" sounds so odd to me that it almost sounds incorrect. But I have heard people from other states say "clothes store" before. It's just a regional difference like whether Pepsi is called 'soda' or 'pop'.