That would require a Japanese history buff to answer, luckily I am one! The main difference between a haori and a hanten is that a haori has a collar, and of course, more colorful designs. That’s because the haori was something noble/rich Japanese wore as more ‘official’ wear, like the suits we wear nowadays, while a hanten was what the commoners wore starting from the Edo period, thus the difference in variety of designs. Today, haori is usually worn over a kimono while hantens are worn by salespeople or as a thicker relaxation wear called ちゃんちゃん(very comfy in the winter btw, I recommend it.) The lines between hanten and haori were blurred in the Edo period with a law that made haori’s illegal in the Edo period, which caused the confusion between the two as people blurred the lines to circumvent the rule.
TLDR: Hanten is more work/casual, haori is more formal, ergo the colorful designs
hope this helped!