It's quite simple. Marketing is a push, branding is a pull.
Marketing puts new products out into the world and helps people solve new problems. It gets the word out. It tells how this product will change a user's life. Marketing is the act of putting new things out there.
Branding makes people care about what is being marketed. It is the heart and soul, the personality that makes a marketing effort more likable than the next. Branding makes things that are marketed attractive.
If you don't do a good job marketing, no one will know.
If you don't do a good job branding, no one will give a shit. You need both and they must feed off one another. They are two sides to the same coin.
The Nike swoosh, the Apple apple, the Target bullseye. All of these logos are recognizable in an instant and yes, it took a while for them to get there, but there is a common thread between them oft-overlooked in the success of their brand identities:
They have good names.
Since the name of a brand is further up in the headwaters than the logo, it makes sense that a crappy name will hinder the success of the visual identity. Don't believe me? Well, let's try these with different monikers.
Nike -> Elegant Running Solutions.
A swoosh would not fare well under this.
Apple -> Creative Computers, Inc.
Why the hell is the logo an apple?
Target -> Minneapolis Market (Target started in this city)
The bullseye loses all gusto.
You get the picture. Brand identities, just like people's identities include a lot from the name. Why do you think authors and screenwriters obsess over the names of these characters they create? It matters and there is an emotional value to the name of a company.
If you don't nail your name and have it aligned with the emotional value you want to manifest within your audience, your identity as a whole will suffer. How do you do that?
Define your brand.
Alright, say you want a logo for your startup. For an experienced designer, this has a streamlined process as well as varying tiers of engagement. They also have a rate for which they will carry these services out. Unless added variables outside of these packages are added, the price shouldn't change that much.
Now say you want a custom e-commerce website, with a bunch of third party integrations, some help on copy, sourcing photos and icons, and then recurring maintenance. You don't know how many pages there are, who is responsible for a lot of the things that will go into the site, it's all custom.
Here's the thing, some design work can be structured within a detailed process. Projects like that should have fixed prices based on the value the designer is bringing to the table. Projects that are unique and require just as much planning as they do execution get custom prices.
In the instance of the latter, it makes sense to dedicate 10% of the estimated budget to getting three, tiered, custom options.