W[n_,m_]/;f[n]==g[m]:=1
W[n_,m_]/;f[n]!=g[m]:=2
Table[W[n,m],{n,1,4},{m,1,4}]

W[n_,m_]/;n==g[m]:=1
W[n_,m_]/;n!=g[m]:=2
Table[W[n,m],{n,1,4},{m,1,4}]

n = 4;
ConstantArray[1, {n, n}] + Unitize[Outer[Subtract, f /@ Range[n], g /@ Range[n], 1]]

n = 4;
SparseArray[{n_, m_} /; f[n] == g[m] :> 1, {n, n}, 2]