Let's use breakers as an example. If you subject a breaker to a current that is above its interrupting rating, then the heat generated in the breaker's contact points may cause them to fuse together. At that point, the contacts will no longer be able to open, and the fault will have to be terminated by the opening of some other breaker. That is what 110.9 is addressing. Please note that this is all about the breaker itself. The question is how much current can it handle without self-destructing.
What 110.10 requires is that the breaker be selected so as to enable it to open in time to protect the downstream equipment against damage. The selection process would take into account the characteristics of the circuit. Such things as wire sizes and lengths, along with voltage levels and the impedance of the service transformer, all go into the calculation of fault current that is available at the location of the served equipment. Here the emphasis is on the served equipment. It will have a maximum fault current that it can endure without being destroyed. We need to design the circuit and select a breaker so as to prevent the fault current from getting that high.