They are not the same, but related. From Wikipedia (article "gas constant"): " [The gas constant] is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) per temperature increment per mole (rather than energy per temperature increment per particle)".
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Boltzman constant
No, the gas constant, or any constant, is constant meaning it doesn't change.
Boltzmanns constant
"Characteristic Gas Constant"The constant 'R' used in the characteristic gas equation PV=RT , has a constant value for a particular gas and is called 'Characteristic gas constant' or 'specific gas constant' . Its value depend upon the temperature scale used and the properties of the gas, under consideration.The value of R will be.For atmospheric pressure air,R= 287 J/kg/k
a simple model that describe the distribution of velocity of molecules in a gas with probabality concept. according to this model the probability of finding a certain velocity in a gas is proportional to e-E/KT, where E=1/2 mv2 for a free atoms of a gas.