  Alain Connes' construction of the standard model is based on a generalized
Dirac-Yukawa operator and the K-cycle $(\HD ,D)$, with $\HD$ a fermionic
Hilbert space. If this construction is reformulated at the level of the
differential algebra then a direct comparison with the alternative approach by
the Marseille-Mainz group becomes possible. We do this for the case of the toy
model based on the structure group $U(1)\times U(1)$ and for the $SU(2)\times
U(1)$ of electroweak interactions. Connes' results are recovered without the
somewhat disturbing $\gamma_{5}$-factors in the fermion mass terms and Yukawa
couplings. We discuss both constructions in the same framework and, in
particular, pinpoint the origin of the difference in the Higgs potential
obtained by them.
