Most people in marketing or advertising don't even know the difference and a lot of times just use them interchangeably.
But there are two different things that require to different types of thinking.
Marketing is the thinking - its the big idea - it's the change and impact that the business seeks to solve for.
Advertising is the voice. It allows you to get heard over everyone else.
People think they can do both - you can't. Not at the same time anyways...