Both true but there are limits. Grad students are still defined by what they've done previously so while there is a lot of choice, it's still within a particular field (i.e. limited to a subset of the whole 'PhD-space').

That's probably stating the obvious (but sometimes it's worth doing that).

Edit: The analogy does works but you might want to consider subjects as 'startup areas' e.g. consumer, enterprise, infrastructure, etc