What is the difference between clothing brand and fashion brand?

They are essentially the same, but there could be some differences if examined closely.

Clothing brand is a brand for clothing, such as shirts, trousers, skirts, dresses, jackets, ties, and any other wearable garments.

A fashion brand is more encompassing. It includes clothing, in addition to jewelry, accessories, shoes, makeup, perfume, handbags, and possibly other design elements such as home and vehicle interior items. Fashion brands include anything the fashion designer wants to design.