Every website we have built since 2011 has been “responsive”. Responsive means that your website resizes itself to display on the different devices. We even change the Menu structure on most sites so it is much easier to navigate on smaller devices. Often we change the home page appearance as well because the information someone wants when they are looking at your website
In most cases you don’t need a second website for mobile devices. In fact have a website that is responsive helps your rankings by bringing all of your potential to the same location. Google then sees your website as an “authority website”. If you dilute that traffic by sending a percentage elsewhere then you dilute your changes of ranking well.
Oh and don’t believe the sales messages that seem to be going around at the moment where Google gives preference to mobile only sites when people are searching from a mobile phone. I had a great laugh when I heard that one. Try it yourself, search on your computer and see what results show, then search on your mobile phone and so long as you are in the same location you will get the same result.