Options in Customizer are in charge of appearance of your site. You can control various features of header, footer, font, color, logo, menu, etc here. Remember that any adjustments made by you will become real with the condition that you have clicked Save & Publish button on top.
Site icon is an image viewable in browsers for users to identify your website among many tabs. Please remember that the icon must be square and at least 512px wide and high. See the illustrative image to better understand function of the site icon. After choosing the image , you will click Save and Publish. Then when you come back to your site, you will see an image displayed on the tap of your website. It is clear that by dint of the this icon, you can distinguish your website`s tab from other tabs more easily.