OK, we need to come clean here a bit with terminology, before we can talk content:
Prior to RedHatRHEL 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 RedHatRed 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 unixUnix-like SystemVSystem V?
None, "SysV" is really just a shorthand for "System V". And both are not RedHatRed Hat Linux, nor is RHthat a descendant of them. (And, System V isn't only "unix"Unix-like", it is a commercial UNIX by AT&T.)
In other words, RedhatRed Hat (and basically all other Linuxes of the day) used the init concept from SysV, by using the Miquel van Smoorenburg's sysvinit program from the GNU project. 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 SystemVSystem V in RedHatRed Hat Linux (we know that, because otherwise SCO would have tried to sue the hell out of RedHatRed 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!)