Voltage regulator vs. voltage reference
A voltage regulator is designed to take a variable voltage in (say, 2-5v), and output a constant voltage (say, 3.3v). Now, voltage regulators are typically used to power a circuit, which means they will have a current output of a few hundred mA or more, generally speaking. In order to keep cost, size, etc down, the output tolerance on voltage regulators are (again, generally) a few 10s or 100s of mV.
For example, the RG71055 voltage regulator has a minimum output voltage of 5.2v, and a maximum of 5.8v, with a target output voltage of 5.5v, and can source 30mA. That's about a 5% voltage tolerance, assuming I number crunched correctly.
On the flip side, a voltage reference is designed to take a variable voltage, and deliver EXACTLY the rated output voltage. For example, the LT1790 can supply 5v with a tolerance of 0.1%, which is a 50x improvement over the RG71055. However, the LT1790 can only source 5mA max, which is 6x less than the RG71055. A voltage reference is used when you need to know that this line is exactly a certain voltage (in other words, really tight tolerances). On Digikey, you can get a voltage reference with 0.01% tolerance. With voltage regulators, you'd be lucky to get one with a 1% tolerance.
Generally (though there will be exceptions) references have better specifications than regulators. Included in those specifications are ...
temperature stability
input voltage stability
output load stability
(stability is a big thing with references!)
output noise
... as well as initial accuracy. Though you will often find that some references have various grades, and better initial accuracy is available in the higher grades, at a cost!
Of course, what a regulator will do is supply a large output current. References vary from low output current, to essentially none. Check the specifications for how much current it's rated to deliver, while maintaining its specified accuracy.
One additional (to your other answers) factor -- some regulators have a minimum current below which they're not specced to perform. This is similar to and may in fact be higher than the maximum current available from a reference. Thus if you need a voltage for reference (i.e. you're drawing next-to-no current from it), you need a voltage reference. (For a regulator I based this on LM317, which is probably close to a worst case being both an old design and adjustable)