The simple definition is a mono uses stressed panels whereas the tube frame uses... tubes. Ian's explanation is excellent (using roof, inner fenders, floor pan, etc. to bear the loadings).
I believe the principle advantage to their adoption was that comparable chassis rigidity for a lighter weight at a lower cost. The alternate mode of construction when the mono gained popularity was the body on frame construction (think "truck") with a few outliers like Lotus who used spaceframes on some and their backbone structure on others. The backbone has a very strong structural member connecting the front and rear suspensions and drivetrain. This pic shows the concept for the Delorean, another backbone car:
I believe structural advantages (rigidity), lighter weight for given structural properties, and cost to manufacture drove the change from body on frame to mono's.
As to repair vs. replacement of damaged mono's, the structural integrity of the tub is based on its material properties (though now that I wrote that, it seems rather obvious). The strength of a fiber-based (say, carbon-fiber or kevlar) depends on a number of things, basically summarized by saying the fibers can't be broken and additionally the resin or bonds between the different layers can't delaminate. If the fibers are broken or the bonds between the layers of fibers are compromised, you can't "weld in" another piece. The fiber-based mono's are particularly susceptable to damage by impactive forces due to the material's catastrophic failure mode (they don't bend much and are strong enough to take a lot of force, but when they DO break- BANG, all the force they were holding tears them apart). I'd be very hesitant to get in a patched up tub and strap in.
Metal mono's are different as their material properties allow deformation (useful for absorbing energy of impacts as well as straightening after an incident). If you bend a metal mono, the panels can (theoretically) be either straightend or removed and replaced. You may remember
this thread showing the restoration of Jim's T70. His concerns with the mono were able to be repaired by replacing panels:
Had this been a carbon-fiber mono, this would not have been an option. As for what to do with carbon fiber mono road cars, I would assume the same criteria would apply. Check for damage and if any is apparent the whole mono would need to be replaced.
Sometimes even a metal mono is bent beyond saving. They can be pulled back into shape fairly closely but the ability to get all the dimensions within factory spec may not be possible. When insurance companies "total" a car, they figure the cost of paying someone to remove and replace the stuff that's way off is less than the cost to provide a new car and hence it's "unrepairable." Technically everything's repairable but not always economical. This would actually apply to mono's or a spaceframe.
Long winded but hopefully helpful...
Chris
