This is a common question.  The two terms are used interchangeably they are similar but they are also different.

Personal branding helps you to show potential customers who you are. You can only put so many smiley faces and emoticons into a post or message to show just how fun you are! Personal branding photos show you personality, your personal style, when you do in your spare time, and just you! 

Business branding tells the story of your business — Who you are as a business, what you offer, how you perform your job or how you create your product. It could be a styled session to showcase your product’s placement in your client’s home or a session showcasing how you serve your target client.