It often depends on the company. I've been a web developer for nearly 20 years and in the course of my career I've had titles like "Senior Software Engineer" and "Programmer/Analyst."
In my experience, any web developer worth their salt knows about application architecture, algorithms, scalability, distributed systems, version control, databases, data migration, APIs, testing, and on and on.
It's the companies who realize a good web developer is a software engineer that often use that title whether you are building web applications, embedded software, etc. In these cases, Facebook/Google may very well have web developer positions for hire under the "Software Engineer" title.
I have to respectfully disagree with @cdagli. As developers, we all face problems that are already solved. A good developer knows how to evaluate the existing solutions and determine which ones are well done and evaluate when their time is better spent building their own. Or, contributing to open source solutions that meet some of their needs but lack in other areas. If doing unique work was what made someone a software engineer, then there wouldn't be many of them out there.
Also, unlike @cdagli, it's been my experience that a Wordpress developer can be responsible for custom development, integrating with 3rd party systems, and other "software" oriented roles. It's the platform itself that gets a bad name due to many poor implementations and how easy it is to get started but there's a big difference between an editor who builds pages in Wordpress, Drupal, etc. and a developer who implements custom solutions built on these platforms.
If companies were to think like that, then a Java developer who deploys some of his apps on Heroku isn't a software engineer. Slack uses a ton of PHP for server-side application logic in their infrastructure. I bet the developers behind their codebase are considered software engineers. Just my 2 cents but I wouldn't assume every web developer is just building Wordpress pages.