When you get a dialog box like this:

you can hit Enter to “press” the blue button.

However, you can also hit the tab key to move the focus ring to another button:

then hit the spacebar to “press” the button that has the focus ring around it.

Enter hits the blue button, spacebar hits the focused button.

Many dialogs also have command key shortcuts, and some will display the keyboard shortcut when you hold down the command (or Apple, or cloverleaf) key.