Terminology for describing nuclei participating in metallic bonds I've read many times that in metals (for example sodium metal), what constitutes the crystal lattice is an arrange of atoms, since no electron is given or lost, they are just shared between all the atoms within the structure.

In other texts though, it is written that metallic bonding is comprised of cations "surrounded" by free electrons since electrons are not held to the nucleus as in a single metal atom in the gas phase. From a formal point of view, which of the two statements is correct? Does it make a difference to consider cations or atoms when describing metallic bonding?

Which is the more appropriate terminology?
Both your statements mean the same thing, however it is convenient to think of metals as kernel + sea of electrons, as it greatly simplifies visualization, conceptualization and thus calculations. From a purely numeric viewpoint, i prefer the 'sea of free electrons' model or that cations are surrounded by free electrons.