#"Covalent bonding"# specifies the sharing of electrons between two given atoms; and the modern covalent bond is conceived to be a region of high electron-density between 2 positively charged nuclei, such that nucleus-nucleus repulsion is negated, and a net attractive force results. Covalent bonding can be invoked for both molecular, and non-molecular materials,
On the other hand, #"metallic, and ionic bonding"# are characteristic of NON-MOLECULAR materials. Ionic bonding results from the transfer of electrons between species to form discrete positive and negative ions. The ions arrange themselves into an ordered lattice such that each cation is electrostatically bound to each anion in the LATTICE, and vice versa for the anion. The non-molecular nature of the interaction gives rise to high melting points, a lack of electrical conductivity in the SOLID state, and brittleness of ionic materials.
Of course, each cation is electrostatically REPELLED by every other cation in the lattice, but if you sum up electrostatic attraction versus electrostatic repulsion over the ENTIRE lattice, which can certainly be done quantitatively, a strong, net attractive force persists across the entire lattice.
And metallic bonding is typically described as #"positive ions in a sea of electrons"#. Here, a close-packed array of metal atoms, each donate 1, or 2, (or more) electrons to the entire lattice. The metal ions, which are of course positive, are attracted to the electron sea, and the non-directionality, and non-molecularity of the attraction results in typical metallic properties: #"(i) malleability; (ii) ductility"#, the ability to be beaten into a sheet, and drawn into a wire; #"(iii) electrical and thermal conductivity,"# for which the free electrons are also responsible, and also #"(iv) metallic lustre"#.
