The global styling options will apply to your entire website at once. If you want to change the colour of the font everywhere on your website, you can do it from the Global Styles settings. That way you don't have to go to every text element on your website and change the colour manually.
The styling options that are available on the element level will only apply to that element and will override the Global Styles. That means that if you want a specific size for a Header on a page, you can edit that specific element without changing all other Headers on your website.
That also means that if you have applied a style for a Header on page A and then go to your Global Styles to edit all Headers on your website, the global style will not apply to the header on page A. You would need to reset the styles for that Header if you want the global styles to apply to it.