First there was the web. The web meant 640x480 and then 800x600px target resolutions. And it was good.
Then we upgraded. Widescreen. 1024x768. 960 grid systems were everywhere.
CSS2 had media types. CSS3 has media queries. Designers started caring about browsing on mobile devices after the iPhone launched. You have the mobile app and you have the website and there's a need to kinda make them 'feel' similar, but that's it.
Responsive design flourishes and ushers in the era we currently enhabit.
What Are We Designing For?
"Mobile First" seemed to be the biggest battle cry in 2013. Remember when Bootstrap 3 came out? They even changed their approach to mobile first. Design small and scale it up.
Brad Frost advocates 'atomic' design, which is more focused on the elements themselves and are device agnostic.
Nowadays, people are taking a more nuanced approach. This leads to much better results. To quote a great article on this, "it is not accurate to assume that mobile is the primary experience". Smashing calls is "Journey-Driven Design" which is just a fancy way of talking about applying user-centered design techniques based on your target demographic.
Isn't It Just Semantics at this Point?
The user journey is never as simple as we think it is when we are creating documentation for clients like personas and user flows. Examples can really flesh this out.
Let's think about my user journey for buying a pair of shoes. I see some shoes I like while watching Netflix on my TV. I whip out my iPhone to Google what brand/model shoes they are. I find the answer on Reddit. I click on the link and I see the manufacturer mobile site. Yep, those are the shoes I was looking for.
The next day on my lunch hour, I browse the manufacturer site on my iPad (via 4G) to see better images of the shoes and all the specs. I then go to Amazon and Zappos to read reviews as to the durability and fit. If they run a half-size small or if they wear out prematurely, people will DEFINITELY be screaming about it there. Things check out and I decide I'm gonna buy a pair.
That night, I get on my home computer and price-compare. I've got a 27" iMac, so I can pull up several different sites and quickly tab between each and use the full-width of the interface. I check eBay, Google Shopping, Amazon, and several shoe-centric sites. I settle on the best price vendor that also offers free returns for 14 days, just in case they don't fit. My payment info is saved in Chrome, so checkout is easy. I've got a browser extension that automatically found me a 15% off coupon code and applied it. I click BUY and get a confirmation page and email.
This is a real-world journey map. It doesn't help the shoe company much, since all I did with their eCommerce site (which offers free shipping and returns, but makes you pay full retail price) is land on their product detail page from a search engine result and click through the color swatches and high-res images to be sure the details looked good.
What's the takeaway?
Just Do Your Job
Your site needs to do its job on whatever device you're looking at it on. As a user, I only notice if something isn't working as it should or if it is completely effortless to use and the interface blows me away. The latter only happens in native iOS apps, on my iPad (mobile web that's gracefully touch and swipe friendly), and on a giant desktop (portfolio sites, immersive web apps, etc).
If you're a blog, let the content do the talking. Blogs succeed because they have great content. At the same time, many blogs succeed IN SPITE OF their web design / interface. I'm not the only one that has transitioned over to RSS aggregators or mobile Safari's 'Reader' mode.
The focus on 'mobile first' is kinda moot at this point. Does mobile first work for your users? Cool. Do that. Does your web app not make sense to use on mobile? Does it make more sense to have a desktop / iPad web app and a native app for use on small screens like phones? Cool. Do that.
At the end of the day it's about what it always has been. Giving the best experience possible to your users.