The brief answer: e-mail marketing is a part of marketing automation.
Marketing automation tools can do everything e-mail marketing tools can do but have extra features. Marketing automation practices are quite different from e-mail marketing practices though.
E-mail marketing is often used by companies to get their brand message across to their customers in a cheap way. They inform their leads or customers that they have new products or promotional offers. It is one-to-many and far from a dialogue. Rough segmentation based on gender, age, buyer category is applied. Personalisation is often limited to the use of the name of the receiver.
Only behaviour within that campaign is taken into account.
Marketing automation starts where e-mail marketing stops: First general newsletters are automatically generated based on new content. Gradually, newsletters are replaced by multi-channel, relevant interaction with the consumer, based on a 360° profile of the consumer that is enriched with all the relevant information that a company can obtain like web behaviour, transactional data, personal data, and this combined over all historic interactions.
Although e-mail marketing has become a lot more personalised over time, the content is still very general. As a consequence, the content often tends to be less relevant to the receiver. A lot of e-mail marketing tools have added some marketing automation features, what makes the line between them blurry. A good example is web tracking, that has become a standard feature.
Marketing automation can use the following channels:
SMS (inbound and outbound)
Phone (inbound and outbound)
Beacons and geolocation
Kiosk in shop
Scoring will be one of the other main differentiators: In marketing automation, scoring cards are used for advanced segmentation. Different behaviour like webpage visit/click and e-mail opening/click will give scoring points to the leads and customers.
Marketing automation tools that focus on lead generation will have built-in SEO tools to optimise traffic on website and landing pages.