OK, we need to come clean here a bit with terminology, before we can talk content:
Prior to RHEL 7, their distributions were built on SysV
No. SysV is short for "UNIX System V", and it's a 1983 UNIX operating system, not related to Red Hat Linux.
You thankfully clarify that you mean a "manager". I'd call it the "init system"; and the Linux world usually calls what you mean "SysV-style init
"; not just SysV (because SysV is an operating system suite, not just a boot process manager).
So, that already answers part of your question:
But what is the real difference between SysV and the Unix-like System V?
None, "SysV" is really just a shorthand for "System V". And both are not Red Hat Linux, nor is that a descendant of them. (And, System V isn't only "Unix-like", it is a commercial UNIX by AT&T.)
In other words, Red Hat (and basically all other Linuxes of the day) used the init
concept from SysV, by using the Miquel van Smoorenburg's sysvinit
program. Which was, according to its Changelog
file, originally a primitive port of the concepts of the System V init process to Minix. There's no System V in Red Hat Linux (we know that, because otherwise SCO would have tried to sue the hell out of Red Hat etc).
Why did they call it SysV, if it's the same?
It's not the same. They don't call it SysV, they call it SysV-style, because it reuses concepts from UNIX System V from 1983. (that even rhymes!)