In the early days it was easy to choose which you needed as a web designer designed how the website looked and the web developer made the website work.
Often the designer and developer would work together on the website in order to get the best result.
These days, it doesn't quite matter so much. A designer will sometimes be able to code and a developer will more than likely also be able to design.
The thing to concentrate on mostly when you are choosing is the portfolio that they are offering.
With the designer, you need to check on how their website works and if the've developed it themselves or if they've used plugins and themes to achieve what they have presented to you.
If you don't like the look of the design, the developer probably won't make your site look like you want it to, however sometimes it may be worthwhile as the developer may be able to customise the backend to your liking a lot more than the designer will.