It's not really that different from how things were 20 years ago. There's a few bells and whistles added now, but for the most part it's still the old sequence.
(added this comment because of the "modern" qualifier in the title)
(added this comment because of the "modern" qualifier in the title)
At the broad level, though, yes absolutely. Unixes with System V init have been drawing a distinction between 'single user' boot activities like fsck'ing the filesystems and 'multi-user' ones like starting daemons for a long time, so that's a two stage boot. Linux booting became three stage once it added initial ramdisks so that the core kernel didn't have to have to build in all of the pieces necessary to get the root filesystem.
(I'm the author of the linked-to entry.)
Ironically, 20 years ago was almost three years after van Smoorenburg init+rc had diverged from the old idea of one "single-user" mode and had instead taken the route of two modes, emergency and rescue. In fact, we only need to wait a year or so until it has been 20 years since those names can be found in widespread use. It has already been more than 20 years since the name "emergency" gained traction.
* http://jdebp.info./FGA/emergency-and-rescue-mode-bootstrap.h...
So whilst things are like they were 20 years ago, how things were 20 years ago isn't in fact the old AT&T System 5 world that people nowadays tell one another it was. That was the 1980s, and it wasn't Linux-based. Indeed, by 25 years ago the AT&T world itself had already introduced ideas changing the original model of multi-user login, such as the Service Access Facility.