What is the combination of lenses, that can achieve what a superzoom
camera like Nikon P1000 can do (125X zoom)?
Realistically? With an APS-C or full-frame dSLR? There is no such combination. The P1000 is something of an exotic camera.
Let us say a DSLR lens has range like 40mm-320mm. I believe this means
8X zoom. However, 30mm-240mm would also be 8X zoom. So what would be
the difference between these two lenses?
Correct. "the ___x zoom" factor is only a relative measurement of how magnified the image can lenter link description hereook, and is a very simple calculation of how much longer the long end of the lens is from the widest.
Focal length is an absolute measurement and is a physical attribute of the lens. So, a 30-240mm lens could show a wider view at the 30mm end of the lens, but can't "zoom" as far in as the 40-320 could at 320mm. This online Nikon lens simulator can give you a sense of the effect of focal length on the coverage of the view.
But. The field of view you see for a given focal length also depends on the size of the sensor. Think of the focal length as having a film projector a certain distance from the wall, and the sensor size as the size of the screen on the wall. The smaller the sensor is, the smaller the image is and the more it's "cropped" vs. a larger sensor.
How much it's cropped can be given by a "crop factor" which gives the proportionate cropping vs. a frame of 135 format (35mm film; 24mm x 36mm). The bigger that crop factor is, the more "zoomed in" a given focal length will look. But the focal length itself isn't changing.
The P1000's lens has an actual focal length of 4.3-539mm. But the 1/2.3"-format sensor it uses has a 5.6x crop factor, which is why the equivalent focal length (i.e., what a full-frame camera would have to use to get similar scene coverage) would be a 24-3000mm.
Canon once made (from 1993-2005) a 1200mm f/5.6 supertelephoto lens for the EOS mount. It cost $150,000, was built-to-order, and took about 18 months from the time it was ordered to be delivered. You don't even want to think of their 5200mm lens. See pixelpuck's "Battle of Biggest Zoom Lenses Ever" article and possibly Roger Cicala of lensrentals demoing the support you need for supertelephotos on youtube.
Nikon essentially took what would be a supertelephoto lens on a dSLR and then put it on a tiny-sensor camera to get insane magnification.
What be the pros / cons / limitations of using a single camera like
P1000 vs a combination of lenses to achieve superzoom photography
(apart from quality of course)?
Pro is it's a single device and only $1000 (about the cost of a supertelephoto lens for a dSLR/mirroless system) that gives you more "reach" than you could get with interchangeable lenses.
The cons/limitations are going to be a small max. aperture (f/8) at the long end of the lens (so perched/standing/sitting birds fine. Birds in flight, not so much), that it's bigger/heavier than many interchangeable lens combinations, let alone other 1/2.3"- or 1"-format (2.7x crop) sensored superzoom bridges [e.g., an Panasonic FZ80, FZ1000 or Sony RX10]) [it weighs over 3 lbs], the need for stabilization/tripod if used at the long end (handholding is possible, but problematic), and all the image quality compromises that with a superzoom range in a lens. And the 1/2.3"-format sensor's ISO performance combined with the slower lens means low light shooting won't be easy.
See also this review of the P1000 for handheld wildlife use.