The parallax range is a way to quantify the amount of stereo depth in an image. It is the difference between the parallax of the farthest object and the parallax of the closest object.
For exemple, if in my image the farthest object has a parallax of +1%; and the closest object a parallax of -2%, then the parallax range in that image will be 3% (+1 - -2).
And if the farthest object has a parallax of +2% and the closest a parallax of 0%, then the parallax range is 2% (2-0).
For small screens, for most shot the recommended parallax range varies from 1.5% to 3%. The rules of the 3D channel Sky 3D recommand that the 3D should be most of the time between +2% for far objects and -1% for close objects (that's 3% parallax range). They say that some rare shots with special depth effect could be as deep as 6.5% parallax range: +4% for far objects, -2.5% for close objects - these are very powerful values. For more details, see http://introducingsky3d.sky.com/a/bskyb-3d-tech-spec/ .
For bigger screen, theater screen or IMAX screen, smaller parallax ranges are often recommended: from 0.75% to 1.5%.
Naturally, the exact appropriate parallax range depends on each shot, and depends on the effect the director wants to achieve.
The expression « Depth Budget» is widely used, but may be ambiguous. In most cases, it is a perfect synonym of “Parallax Range”. It is also often used in a more vague, less mathematical way: it just means “the impression of depth” of the image: one may say “this shot has more depth budget than this shot”, without actually referring to percentage or pixel values.
A more problematic use of “Depth Budget” is when people refer to the “depth budget of a whole movie”: some stereographers think that a movue should have a limited total depth budget, that you can “spend” to vary the depth of the shot: for exemple, if I've done 20min of very soft 3D, with almost no depth, then I have a lot of “depth budget” to spend, and I can make 2min of very strong 3D. Conversely, if I've done a sequence with 10min of strong 3D, then I don't have much “depth budget” to spend for the end of my movie, so I have to make very soft 3D for the ending of my film.
For that reason, and beacause we'd like to be as precise as possible, we chose to not speak about “depth budget”, and we always used “parallax range” to speak of the exact amount of stereo depth in a shot.