Unix and Linux have a common command structure, similar command
shell environments, common set of standard utility programs, games,
development tools, functions, manual (help) file format. They do
not have a common history.
The Unix System Program was original developed at Bell
Laboratories by Dennis Ritchie and Ken Thompson in 1969. It was the
property of AT&T (or some branch of it), was free with source
to educational institutions and was later offered commercially for
DEC PDP computers for 12 to 20 thousand dollars and more depending
on the installed computers. Unix and BSD (a free derivative of
UNIX) were licensed and ported to various other systems vendors
such as DEC (ultrix, osf/1, TRU64. etc), SUN (sunos), Microsoft
(xenix), IBM (AIX), HP (HPux), Apple (OSx), and many more. BSD
itself had a whole bunch of different free implementations under a
BSD license.
There was also a lawsuit between BSD and Novell (which had
purchased ownership of UNIX) claiming BSD should not be giving away
BSD UNIX for free. It ended with BSD allowed to continue its free
licensing after making some changes to its software base.
Linux was a result of an independent project by Linus Torvald
with a small group of independent hackers that became very popular.
He developed a kernel system program that was compatible with UNIX
but was written independently of UNIX, had no UNIX code in it, was
not subject to a UNIX licensing issues, and was distributed under a
GPL license. The Linux kernel together with some independently
written programs, together with many free programs borrowed from
BSD constitute a Linux distribution.