A very common feature of a lot of web design agencies is that they will claim that they can do everything, from web design, to web development, search engine marketing, pay per click and even email marketing. Unless the agency is huge with lots of specialist departments, it is highly unlikely that they will be specialists in all areas.
Web design requires a creative flair and being able to use graphics packages. Good web designers usually have an artistic bent and training.
Web development on the other hand involves being trained in computer programming and knowing various languages and technologies. It involves being able to program efficiently in languages such as PHP, C# and Java as well as how to interact with databases such as SQL Server and MySQL.
There is a degree of cross over. Both designers and developers are likely to be efficient at registering a domain name and setting up hosting but it is useful to think of designers as people dealing with the "front end" the things that look nice in your web browser and the developers as the people who are making it all work behind the scenes.
It is common for a digital agency to have specialists in both design and development however you may find that a one man operation is unlikely to offer top quality in both.
Then there are the Search Marketing specialists which splits into Pay per Click and Search Engine Optimisation. Both of these niches require a full time job to keep up with the latest news. PPC specialists need to acquire the qualifications for the large Ad agencies and SEO specialists need to keep up with all the latest news on changes in algorithms to provide the best possible services to their clients.
It is impossible for a single person to claim to be a specialist in all fields be wary of anyone claiming to do so. Investigate how they can provide all services. It may well be that they outsource to other agencies to provide the other services which is a great solution and gives you a single point of contact however make sure you have the full picture before signing on the dotted line.