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It is shown that in the spin-charge-family theory, as well as in all theKaluza-Klein like theories, vielbeins and spin connections manifest in$d=(3+1)$ space equivalent vector gauge fields, when space with $d\ge5$manifests large enough symmetry. The authors demonstrate this equivalence inspaces with the symmetry of the metric tensor in the space out of $d=(3+1)$ -$g^{\sigma \tau} = \eta^{\sigma \tau} \,f^{2}$ - for any scalar function $f$ ofthe coordinates $x^{\sigma}$, where $x^{\sigma}$ denotes coordinates of spaceout of $d=(3+1)$. Also the connection between vielbeins and scalar gauge fieldsin $d=(3+1)$ (offering the explanation for the Higgs's scalar) is discussed.

Gauge fields with respect to $d=(3+1)$ in the Kaluza-Klein theories and in the spin-charge-family theory