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Is there a difference in the definition of a virtual address space and process address space or can they be used as synonyms?

Sometimes it seems, that process address space means only the memory that is really available to the process and the processed is allowed to access instead of the whole virtual address space.

Understanding the Linux Kernel:

The Process’s Address Space: The address space of a process consists of all linear addresses that the process is allowed to use. Each process sees a different set of linear addresses; the address used by one process bears no relation to the address used by another.

Linux Kernel Architecture:

The process address space consists of the virtual memory addressable by a process and the addresses within the virtual memory that the process is allowed to use.

Whereas in Modern Operating systems it is used as synonym:

In addition, in a PAE (Physical Address Extension) mode, which is used on certain 32-bit architectures to increase the process address space beyond 4 GB, page sizes of 2 MB are supported.

Is this defined clearly in any Linux documentation?

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