Well, to begin with some caps, when you remove them from your head, still retain their shape.
Others, when you remove the cap, the crown collapses into limp fabric. As seen by the left image if you remove the unstructured hat from you head and place it on a surface, it will lose the shape it had previously. On the contrary, as shown by the second image, the structured hat is usually able to retain its shape better due to its sturdier fabric.
Why is that? Structured caps will be reinforced with a sturdier fabric called buckram, which is essentially cotton fabric dipped in a plastic-like bath. In the structured hat there a white buckram reinforcement behind the front two panels. For contrast, the unstructured hat does not have the white buckram panels.
What are the trends around these two types of hats? The truth is, usually unstructured hats tend to have a more casual look and are used to acquire a more trendy look.
On the other hand, structured hats tend to give a more sporty look which in turn, becomes better suited for teams and uniforms. Despite their trends, both hats can be worn by anyone who is willing to look good.
Not to forget, people usually want to add their own designs and the best way to do so is through embroidery.