what are the differences between the Brand Strategy and Marketing Strategy?

It is a shame that we don't have a rating for the questions here, if we had one, I would rate this question 5 stars :) In a very short brief, Branding Strategy is about building a unique personality in the market, and how do you want your client to see you if you were a person, covering your relation and associations with him in several perspectives: credibility, emotions, image, loyalty, advocacy ...etc and you can see that all of those are intangible benefits of your marketing strategy and tactics, and a long term strategy.
On the other hand, Marketing Strategy is mostly a tangible benefits strategy, since your goals and measures are attached to leads and sales volume, and can be done in short terms.
Your coming question should be: which one is the sub of the other?! I would say, logically short term shall be the sub of the long term, though right now, several organizations don't consider corporate branding if they are not selling a physical product, but this will be changed soon, and businesses who are not working on there corporate brands will suffer in the current global economic situation.

Branding is strategic.
Marketing is tactical.
Marketing may contribute to a brand, but the brand is bigger than any particular marketing effort.
The brand is what remains after the marketing has swept through the room.
It’s what sticks in your mind associated with a product, service, or organization—whether or not, at that particular moment, you bought or did not buy.
The brand is ultimately what determines if you will become a loyal customer or not.
The marketing may convince you to buy a particular Toyota, and maybe it’s the first foreign car you ever owned, but it is the brand that will determine if you will only buy Toyotas for the rest of your life.
The brand is built from many things.
Very important among these things is the lived experience of the brand.
Did that car deliver on its brand promise of reliability? Did the maker continue to uphold the quality standards that made them what they are? Did the sales guy or the service center mechanic know what they were talking about? Marketing unearths and activates buyers.
Branding makes loyal customers, advocates, even evangelists out of those who buy.
This works the same way for all types of businesses and organizations.
All organizations must sell (including non-profits).
How they sell may differ, and everyone in an organization is, with their every action, either constructing or deconstructing the brand.
Every thought, every action, every policy, every ad, every marketing promotion has the effect of either inspiring or deterring brand loyalty in whoever is exposed to it.
All of this affects sales.
Back to our financial expert.
Is marketing a cost center? Poorly researched and executed marketing activities can certainly be a cost center, but well researched and well executed marketing is an investment that pays for itself in sales and brand reinforcement.
Is branding a cost center? On the surface, yes, but the return is loyalty.
The return is sales people whose jobs are easier and more effective, employees who stay longer and work harder, customers who become ambassadors and advocates for the organization.
http://www.tronviggroup.com/the-difference-between-marketing-and-branding/

Now there's a subtle difference.
Branding is strategic where as Marketing is tactical (it's not a strategy).
Marketing may contribute to a brand, but the brand is bigger than any particular marketing effort.
The brand is what remains after the marketing has swept through the room.
It’s what sticks in your mind associated with a product, service, or organization—whether or not, at that particular moment, you bought or did not buy.

Brand is a "promise delivered". You make a promise to customers and colleagues with everything you do and, to be successful, you must deliver on that promise every single time. The idea that a brand is a badge, a name or a color is just a tiny fraction of what a brand actually is.

 

Marketing is "The management process responsible for identifying, anticipating and satisfying customer requirements profitably".

 

Marketing, then, is an integral part of your brand. It helps you to communicate the promise that you want customers and prospects to know about. Your marketing should also be based on your brand positioning, personality, values and tone of voice that have all been defined and communicated among your staff.

A fantastic question, but need lenthy answers.
I will make it short.
Brand strategy primarily on equity development.
Marketing strategy is to sustain the market growth.
Brand strategy works on both long and short term developments of brand equity and strength.
To simplify, it is like protecting and increasing the asset value.
Marketing helps the brand to maintain and improve equity value through it is sustained market share and growth.
Strategies cannot be confused as both of them require to work in specific terms with clear execution methods though the common objective is same for both.