I think a web developer is someone who builds web pages for companies or some media agencies using Wordpress, e-commerce solutions or things like that. Mostly faces with problems that are already solved and implements that solutions taken from others.
On the other hand, a software engineer is someone who designs and implements unique software and thinks about maintenance, code quality, testing, scaling etc. Mostly faces with problems that are not already solved or needs optimization.
Companies like Google and Facebook needs software developers more than web developers since they are pioneers in most web technologies and mostly their engineers will be the ones that faces with unsolved problems.