From my research, these two have different meanings but aim to do the same thing; make the lives of the end-users better.
Ecommerce is buying and selling online. You can think of Walmart, Amazon, Target, Alibaba, etc. to name a few of the big online relators.
M-Commerce is a subcategory of e-commerce that focuses on purchases being made via a mobile device. This method allows the delivery of electronic commerce capabilities directly in the hands of the consumer. Using M-Commerce, you can gain better customer insights which enhances the customer experience while increasing revenue.