I get the sense that there is a difference between a natural reach of 10ft and a weapon reach of 10ft, namely that you should be able to attack anything within your natural reach, but I can't find anything clear-cut about it.
For weapons, it's made very clear that if they allow you to threaten and attack something 10ft away instead of 5ft, the downside is that you can't threaten or attack creatures adjacent to you.
With a typical reach weapon, you can strike opponents 10 feet away, but you can't strike adjacent foes (those within 5 feet).
Reach Weapons: Most creatures of Medium or smaller size have a reach of only 5 feet. This means that they can make melee attacks only against creatures up to 5 feet (1 square) away. However, Small and Medium creatures wielding reach weapons threaten more squares than a typical creature. In addition, most creatures larger than Medium have a natural reach of 10 feet or more.
Reach Weapons: (...) Most reach weapons double the wielder's natural reach, meaning that a typical Small or Medium wielder of such a weapon can attack a creature 10 feet away, but not a creature in an adjacent square.
But what about natural reach greater than 5ft? Large creature tend to get such a reach. Large tall creatures get a natural reach of 10ft.
Creatures that take up more than 1 square typically have a natural reach of 10 feet or more, meaning that they can reach targets even if they aren't in adjacent squares.
Unlike when someone uses a reach weapon, a creature with greater than normal natural reach (more than 5 feet) still threatens squares adjacent to it.
It threatens... but can it attack? I guess the question here is: is a threatened square a square you can always attack into?
Then there's the case of large creatures using a reach weapon:
Large or larger creatures using reach weapons can strike up to double their natural reach but can't strike at their natural reach or less.
A typical Large character wielding a reach weapon of the appropriate size can attack a creature 15 or 20 feet away, but not adjacent creatures or creatures up to 10 feet away.
This could imply that usually they can "strike at their natural reach or less" I suppose.
This actually seems simpler: reach weapon = can't attack within natural reach but can attack beyond and up to double natural reach.