Below are my Four Truths ©, derived from the front-end work I've done in the past years. Although presented as “facts”, I recognize the need for (differences in) interpretation and perspective. Please share your comments if you have them.
All web pages are by default responsive.
Breaking that is a choice. Example: http://motherfuckingwebsite.com/
Actually, it's strange that “responsive” is the different one. Normal websites are responsive. It's the ones that aren't that should be called non-responsive, or “fixed”. For example, when talking about it in sales.
Constructing a website mobile-first doesn’t cost (a lot) more time.
Mobile-first is a concept. More time might be spent thinking about how to approach for example the CSS, especially when making the switch to mobile-first for the mobile-first time (get it?!).
A good responsive, progressive enhanced website can function well on all devices.
Selecting a range of devices or browsers the website “supports” conflicts with the theories of responsive and progressive enhancement. If built correctly, a site is able to function well on all reasonably representative devices.
It's always a mix.
Is it adaptive or fluid? Mobile or tablet? Phablet maybe? Responsive or liquid? Let's just acknowledge it: it doesn't matter what you call it. You just want a good user experience. You could think of some theories here: liquid means the container has a percentage based width, adaptive is the new responsive, and so on. The thing is: it's just personal interpretations of terms; not everyone agrees. A responsive website will always be part liquid, part fluid, part adaptive, part robot, part human, part monster, part evil marketing scripts.
Please, let's just call it responsive.