What is the difference between Ground and Low?
Take a look at this: -



It's for a 5V logic system and it tells you what the voltage ranges that are acceptable for standard CMOS inputs. 

So an input signal that is below 0.8 volts will be regarded as a low and that is a definite. However, if the signal received is (say) 1V it might still be regarded as a low but there is no guarantee that it won't be regarded as a high.

Then you could take this further and look at what the specifications of a driver and receiver are: -



You should be able to see that a logic driver output has a tighter spec than a logic input and this should make sense.


  What If I ground instead of sending LOW?


You should be able to see that ground (aka 0V) is in the range of an acceptable "low".


  Or similarly what is the difference between Vcc and HIGH?


You should be able to see that Vcc is in the range of an acceptable "high".