I was asked this week, whether, 1) A "mobile type" website is needed at all, and 2) if so, what type? That's a great question and, at least, showed that the asker was engaged with basic website design ideas, or, at the very least, wanting to know. As the old saying goes, "The stupidest question is the one never asked!"
Do I need a mobile version of any type?
First part - "Do you need a mobile ready version of your site?" An unequivocal, "YES!" There is no doubt that a website that is not easily viewed on a mobile device is already at a serious disadvantage. And, with 60% or more searches conducted on some type of mobile device, that puts your business in a bad internet state.
Which type to have?
The 4 types are in the headline - Mobile, Responsive, App, or Nothing. They all work a little differently, and all have pluses and minuses.
This was the first way we did mobile ready sites, and some still do. You'll see a URL starting with m.<domainname>.com. There's 2 main drawbacks of this way. Generally you end up running 2 separate sites (though not always) which means much more work keeping your site(s) up to date and greater potential for mistakes.
Also, mobile sites tend to be severely stripped down versions of the main site. Whilst this has the advantage of fast load times (a definite plus) for anyone familiar with your main site, it can be a source of incredible frustration as so much content has gone. Ebay and Craigslist were 2 glaring examples of this, though both have now gone to apps.
This is the current preferred method. Special code in the site template detects the type and size of device it's being viewed on and adapts to fit it. Depending on the ability of the designer, this is the most seamless transition from desktop to mobile website. And it's exactly the same site with just layout differences, meaning only one site to maintain.
This is our preferred method, and all our templates are built to be responsive. Clients get a very similar looking site (probably 80%+ is exactly the same) and all the content is there.
Apps have become increasingly popular recently. Like Mobile, they tend to be stripped down versions of the main site, but draw their content directly from the main site, so there's, generally, no need to maintain 2 sites. However, being stripped down, they can be frustrating for regular users of the main site. They also require the app to be installed on your mobile device.
You also should provide an app for each platform - currently that's Android, Apple, and Windows. So there can be quite an upfront expense in setting this up.
Don't! Period! Making visitors pinch and swipe to move around your site is bad. Get with technology and give them the best experience you can. Any decent designer can offer you a site that is responsive. If they cannot do this, then you should question what else they aren't skilled in.