Mobile First Web Design
Mobile First Web Design is another way of saying Responsive Web Design.
Essentially, what used to happen was a website would detect your iphone or other mobile device and serve you an alternate set of web pages that were visually optimized for reading on your device.
Now, with Responsive Web Design techniques, the website detects the browser width of your device (in pixels) and serves you alternate "styles" -- as opposed to an entirely different version of your website. (not having duplicate content on your pages is a cornerstone of Built-in SEO.) Responsive Web Design encompasses mobile web design for smart phones and also styles optimized for tablets, small laptops, and other devices no matter what operating system or browser they are running.
Yet Mobile First can still be your focus. Many of our clients have at least parts of their site that are 100% geared to mobile. Perhaps from our standpoint, Mobile First is an inclination applied to Responsive Web Design..