Although not an expert on this aspect... Yet I can briefly outline the difference between SEO and Digital Marketing.
SEO or Search Engine Optimization is the application of procedures while crafting your writings to make them optimized for better rankings in Search Results at Search Engines. The better the rankings in Search Results, the more traffic your site or articles get. SEO involves choosing the right trending topic to write about, using proper keywords in headings and paragraphs, emphasizing keywords, using images with 'Alt Attributes', backlinking your article from other sites and sharing it amongst your social circles.
While digital marketing is a type of marketing to promote your product in the digital world. Digital marketing is done through the use of electronic devices such as PCs, Tablets, Smartphones, Cell Phones, Television, Radio and SMS etc. Therefore Search Engine Optimization becomes a part of digital marketing because SEO is done to promote your digital content online. Digital marketing also includes Social Media Marketing, advertising on the internet and non-internet channels.