I'm comparing it to mineral spirits essentially. Are they the same on wood? Mineral spirits seems to strip off any finishing on wood, will WD-40 do the same?
WD-40 is not equivalent to mineral spirits at all. Mineral spirits should normally be just naptha, where WD-40 has multiple different petroleum base oils, as well as a few other ingredients.
Their compositions can be seen in the material safety data sheets:
Edit: As Allman and Keshlam say, the short answer is it will leave a residue that will be undesirable and most likely hazardous to a new finish.
Is it OK to use WD-40 to clean wood?
I think this is an it depends more than a clear no. I wouldn't ever use it on bare wood, but then I don't think people should use mineral oil on wooden products and that is widely done these days.
I have actually read of WD-40 being used as a finish of sorts for bare wood fairly recently on a blog somewhere, either for refinishing tool handles after the remains of the original finish had been sanded off or to finish new handles.
The one case I think WD-40 would be acceptable to use on wood would be to clean and polish finished wood that was very grimy or greasy, essentially using it as a ghetto furniture polish.
There's something else I think I should cover and that's this:
Mineral spirits seems to strip off any finishing on wood
Actually mineral spirits (UK: white spirit) won't dissolve most finishes once they are dry/cured. Spirit and waterbased stains would be unaffected, it doesn't interact with most varnish (especially modern ones made using synthetic resins), it has zero effect on shellac, most lacquers and all the waterbased finishes I can think of.
It will strip away wax however, because mineral spirits is a solvent for wax. But wax is rarely used as a standalone finish (for good reason, it provides little real protection by itself).
Get a quality spray bottle, fill with Luke warm water, add a couple teaspoons of Dawn.
You now have an amazing cleaner / bug killer / pre wash dish spritzer / insecticidal soap for plants.
WD 40 is paint thinner and fish oil. Not bad for some things, but it will act as a bad finish more than a cleanser on wood.