Firstly, both these factors are equal. The 8.84 factor is when we take measurements in meters whereas the 0.225 factor is when we take measurements in inches.
As for the 8.84 factor itself, it is the permittivity of free space.
In conclusion, you've got only one formula:
Er = C * Distance / ( Eo * Area )
Where C is in Farads, Eo is 8.85418782 × 10-12 m-3 kg-1 s4 A2, Area is in m2, and Distance is in meters. This reduces to the first formula you typed first, with 8.85418782 being approximated as 8.84.