  In general, a finite metric function at the center of a black hole describes
a non-singular spacetime but an infinite metric at the center gives a singular
spacetime, where the former is associated with convergent Ricci and Kretschmann
scalars together with complete radial geodesics, while the latter is related to
divergent Ricci and Kretschmann scalars together with incomplete radial
geodesics. For the charged black hole in the four-dimensional
Einstein-Gauss-Bonnet theory, we find that its metric function is finite at its
center in one region of parameters but complex in the other region of
parameters. The finite case describes a strange spacetime which presents the
Ricci and Kretschmann scalars of a singular spacetime and the radial geodesics
of a non-singular spacetime, while the complex case gives rise to the similar
situation. We verify that the cosmic censorship conjecture is maintained for
the black hole model. Further, we investigate the second-order phase
transition, quasinormal modes of perturbation of a test scalar field in the
eikonal limit, and shadow radius for the black hole and find that the
thermodynamic and dynamic properties depend on the metrics. In this way, we
connect the internal structure with the thermodynamics and dynamics for this
black hole. Moreover, we compare such a black hole of modified gravity with the
Reissner-Nordstr\"om black hole of Einstein's general relativity in these
thermodynamic and dynamic properties.
