The definition is not affected by whether the Turing machine is deterministic or non-deterministic. So PSPACE=NPSPACE. The set PSPACE is a strict superset of the set of context-sensitive languages. The following facts are known, where "<" means "strict subset", and "<=" means "subset" (unknown whether they are equal):
$1,000,000. It is also widely suspected that the <= on the last line should be a <.
The hardest problems in PSPACE are the PSPACE-Complete problems. See PSPACE-Complete for examples of problems that are suspected to be in PSPACE but not in NP.