Actually on Windows a process is a thread with additional information.
The unit of execution is the thread.
On the UNIX world it depends on which UNIX you are talking about.
Linux has a similar model to Windows NT nowadays, hence clone() as key primitive.
Other UNIXes have different approaches.
I worked on the kernel of DEC Ultrix, Mach/BSD and a couple of other early Unixen. The approach in all the ones I worked on was broadly the same.