I don't see that it makes much sense for a device to define a common-mode input range which is larger than the allowable input swing; my guess is that the "input swing" and common mode range both extend 300mV beyond the rails, but describing the input and output swings together as being "rail-to-rail" made it clear that they both extend at least that far (the input actually swinging a little further).
In some cases, op amps may have a common mode voltage range which is smaller than the allowable input voltage swing. In such cases, for correct operation to be guaranteed, neither input may exceed the "input-swing range" [which could be specified differently for each input], and the inputs must straddle at least part of the common mode range. While an op amp will only be able to operate with any precision when both inputs are within the common mode range, having an allowable swing which goes beyond will help ensure that even if input stimuli cause an op amp to go beyond the range where it can operate precisely, it will resume proper operation when input stimuli return to acceptable levels.
To understand why this is important, imagine a hypothetical op amp, used as a voltage-follower, whose common-mode range and inverting-input swing are both limited to +/-10 volts, and which outputs -12 volts when the inverting input is driven with anything below -10V, regardless of what the non-inverting input is driven with. Such an op amp might operate perfectly as long as the input stayed within the range of +/-10 volts, but if the input were to drift even momentarily to -10.1 volt, the output could go to -12V and then be stuck there even if the input went back within range. If the op amp's common-mode range were limited to +/-10V but its voltage swing were specified to +/-12, then an input of -10.1V might cause the output to swing to -12V, but as soon as the input went back above the -10V threshold the output would start tracking the input again.