Believe it or not, I get asked this very question every once in a while. To those in the know the answer is simple but for those that are embarking on their first development it can be confusing.
In a nut shell; these are two different departments with two different applications each requiring different information. Chances are you will need them both.
Sometimes your development will fit into what is called Permitted Development, which is a whole other blog. This is when planning permission is not required. And if this is the case you can skip to the second part of the question; building regulations.
Building regulations is often inevitable. This is a set of minimum standards developed by the government to ensure buildings are safe, warm and suitable for all, plus a few environmental things thrown in to boot. With the right details and specifications, this statutory application process is always approved.
Planning permission, on the other hand, is a consideration of the development in relation to its surroundings and setting. Here appearance matters rather than construction method. Sometimes this application can be refused for reasons that sometimes do not seem fair.
Both applications can be submitted by individuals, lay people if you will, or they can be supported and delivered by an agent; an architect, perhaps. The benefit of using an agent is their experience and education on each subject. An architect can certainly bring value to a project in this regard with sound advice and strong justification.
So, if in doubt about planning or building regulations, the best thing to do is speak to an architect. Not only could they procure both applications on for you, they may even make the process easier and much less stressful for you.