While 'Branding' is Perception, 'Marketing' is Promotion.

Branding is how your product or service is seen, understood, perceived, or recognized by your customers/audience.

Marketing is every activity you carry out through various channels to influence your brand, to grab and hold the attention of your customers/audience.

Marketing brings the customers/audience while branding retains and keeps them in.

Branding is who you are, while marketing is how you build awareness or how people get to know you.

Branding is long-term, while marketing is short-term.

Which Should I Do First, Branding or Marketing?

Can you market before building a brand? 
Can you have a brand when you have not done marketing? 

The best solution is you need to build both at the same time. Your branding and marketing tactics need to be adaptive and change in coordination with each other.

If you must choose, it's usually best to focus on branding first. Think about how you want people to think about your business. Imagine some experiences or emotions they will have when they get involved with you. Then work backward to develop it deliberately in your audience. 

Have a clear understanding of your branding details, then move to your specific marketing tactics. Determine the correct channels on which your brand should create and make sure your brand visuals and tone are well carried out through all of your marketing channels, including your social media and website. Lastly, maintain a presence to engage supporters.