The button label is the text that would appear on a call-to-action button on your website. Think of when you send and email, and you click 'send' the text that reads 'send' would be the button label.
What is a button label?
Button labels inspire the users to take an action. To indicate what a button will do, use the function as the label of the button. When users read the button labels like Save, Preview, and Publish, they know exactly what the button will do when pressed.
What is a button link on Shopify?
A button link on Shopify is a hyperlink that is used to navigate between pages on a Shopify store. It can be used to link to other pages on the same store, or to external pages. Button links are typically placed in menus, and can be customized to match the look and feel of a store.