Bonded bullets have a chemical or metallurgical "bond" between the jacket and the core [dissimilar metals]
Theoretically at least, the core adheres to the jacket, and when the bullet hits bone or flesh, it will not separate core from jacket.
A non-bonded bullet has no such adherence, and in cup and core design, can separate completely. At that point, penetration ceases.
Often, cup and core bullets may incorporate some mechanical means to try to keep the parts together. [Hornady Interlock, Remington Cor-Lokt, etc]
Bonded bullets usually fall into the "premium" category, thus you pay more for them. It is up to the shooter to justify whether this is worthwhile or not.
For light-bodied, thin skinned game, bonded bullets are not really necessary. [Think Deer, Pronghorn, etc] But as the game gets larger, and the bones get heavier,
a case can be made for the advantage of "premium" bullets. [Bonded, Partitions, Monometals, etc] This particularly applies when hunting something that can bite back, lol.
One trend that I am NOT copying is the use of thin-jacketed, non-bonded target type bullets for shooting big game.
I have already seen several "surface" wounds without penetration with this type of bullet.
Hope this helps. Dave.