Unless you make your products yourself, you should always register your products' manufacturers in PrestaShop.
By entering information about the manufacturers, your site's visitors can quickly access all of a given manufacturer's products. This makes navigating around your site easier for them. In terms of visibility, defining the brands will improve your position in search engines.
You do not have to register your suppliers if the brand/manufacturer supplies you directly and you have already registered it. It all depends on what you need, but if the supplier of the product is not the same as the brand, you need to make sure that both are registered, and that they are both associated with the corresponding products.
Just like brands, visitors to your shop can quickly access a list of a supplier's products. This makes it easier for them to navigate your site. In terms of visibility, defining the manufacturers, just like displaying the brands, will improve your position in search engines.