Fork is nothing but a new process that looks exactly like the old or the parent process but still it is a different process with different process ID and having it's own memory. Parent process creates a separate address space for child. Both parent and child process possess the same code segment, but execute independently from each other.
Threads are Light Weight Processes (LWPs). Traditionally, a thread is just a CPU (and some other minimal state) state with the process containing the remains (data, stack, I/O, signals). Threads require less overhead than "forking" or spawning a new process because the system does not initialize a new system virtual memory space and environment for the process.