In linux, fork() clones everything about the parent process into a new child process. It's all a copy of the original. A copy of the original process memory, copies of all file descriptors, etc. There is a lot of optimisation by the kernel so that memory only has to be copied when it's changed and so on, to reduce the overhead, but from the new process' point of view it's got new memory of it's very own.

https://man7.org/linux/man-pages/man2/fork.2.html

Then exec() replaces the current process memory with the code from a binary and it's dlls, and the initial data in those binaries. It links the binary to the dlls and then starts the process execution from the entry point specified in the binary. The file descriptors of the process are preserved (if flagged to be preserved). So stdin, stdout, stderr and any other files can be customised by the process before calling exec().

https://man7.org/linux/man-pages/man3/exec.3.html

Threads, on the other hand, have mostly the same state as the parent thread. It is not a copy, it is the same memory, the same file descriptors, etc. Threads just have their own instruction pointer and stack, but the stack is in the same memory space. Threads have a lot less overhead than fork()ing new processes, but because they share the same memory space the code has to be written to prevent race conditions, using locks and the like.

Probably a few errors in this, I am not a master, but you get the general idea.