The difference between Google AdWords and search engine marketing depends on the context search engine marketing is used.
SEM marketing was the general term for any form of digital marketing that advertised a business and website services, consequently increasing visibility. It includes organic search engine marketing and paid SEM.
But over time, around 2006, the SEM term became widely known and accepted as the standard term for 'paid search.'
Regardless of this, some bloggers still use SEM’s original and general definition. To deter uncertainty, pay attention to the context of the term’s use.
When a person uses search engine marketing in a "paid search" context, it is the same as Google AdWords. Google AdWords falls under the ‘paid’ search engine marketing.