  We show that the Schr\"odinger wave functional may be obtained as the product
integral of precanonical wave functions on the space of field and space-time
variables. The functional derivative Schr\"odinger equation underlying the
canonical field quantization is derived from the partial derivative covariant
analogue of the Schr\"odinger equation, which appears in the precanonical field
quantization based on the De Donder-Weyl generalization of the Hamiltonian
formalism for field theory. The representations of precanonical quantum
operators typically contain an ultraviolet parameter $\varkappa$ of the
dimension of the inverse spatial volume. The transition from the precanonical
description of quantum fields in terms of Clifford-valued wave functions and
partial derivative operators to the standard functional Schr\"odinger
representation obtained from canonical quantization is accomplished if
$\frac{1}{\varkappa}\rightarrow 0$ and $\frac{1}{\varkappa}\gamma_0$ is mapped
to the infinitesimal spatial volume element $\mathrm{d}\mathbf{x}$. Thus the
standard QFT obtained via canonical quantization corresponds to the quantum
theory of fields derived via precanonical quantization in the limiting case of
an infinitesimal value of the parameter $\frac{1}{\varkappa}$.
