We consider reproducing kernels $K:\Omega\times \Omega \to \mathbb{R}$ in multiscale series expansion form, i.e., kernels of the form $K\left(\boldsymbol{x},\boldsymbol{y}\right)=\sum_{\ell\in\mathbb{N}}\lambda_\ell\sum_{j\in I_\ell}\phi_{\ell,j}\left(\boldsymbol{x}\right)\phi_{\ell,j}\left(\boldsymbol{y}\right)$ with weights $\lambda_\ell$ and structurally simple basis functions $\left\{\phi_{\ell,i}\right\}$. Here, we deal with basis functions such as polynomials or frame systems, where, for $\ell\in \mathbb{N}$, the index set $I_\ell$ is finite or countable. We derive relations between approximation properties of spaces based on basis functions $\{\phi_{\ell,j} :1\leq\ell\leq L, j\in I_\ell\}$ and spaces spanned by translates of the kernel span $\{K(\boldsymbol{x}_1,\cdot),\dots, K(\boldsymbol{x}_N,\cdot)\}$ with $X_{N}:=\{\boldsymbol{x}_1,\dots,\boldsymbol{x}_N\}\subset\Omega$ if the truncation index $L$ is appropriately coupled to the discrete set $X_{N}$. An analysis of a numerically feasible approx...