Covalent, but not small
Every covalent substance so far has been a molecule: a small, finite group of atoms with a definite formula. Some elements do not stop there.
Arranging into a lattice was introduced as a feature of ionic compounds. But certain elements bond covalently to their neighbours, and then to their neighbours in turn, until the bonding runs on through the whole solid without ever closing off into a molecule.
Atomic lattice
A lattice in which the particles are atoms joined to one another by covalent bonds, rather than ions held by electrostatic attraction.
The difference from an ionic lattice is what sits at the lattice points and what holds them there. Ionic lattice: ions, held by the attraction of opposite charges. Atomic lattice: atoms, held by shared pairs.
One element, two lattices
Carbon occurs naturally as an atomic lattice in two different forms, graphite and diamond. Both are pure carbon and nothing else. They differ only in how the carbon atoms are joined.
Allotropes
Different structural forms of the same element, in which the atoms are bonded to one another in different arrangements. Graphite and diamond are allotropes of carbon.
Not two elements, not two compounds
Graphite and diamond are the same element. They are not two elements, not two compounds, and not isotopes — isotopes differ in the nucleus, while allotropes differ only in how the atoms are arranged.