Cleavage is structural
Where bonding is weaker along particular planes, a mineral splits along them repeatedly and predictably. Galena cleaves into cubes; halite does the same; calcite, being orthorhombic, cleaves into rhombs that no amount of care will turn into cubes.
Because cleavage reflects structure rather than growth, it is one of the most reliable identification tests available.
Fracture is what is left
Minerals with roughly equal bonding in all directions have no cleavage and fracture instead. Quartz shows conchoidal fracture, the curved shell-like surface familiar from broken glass and worked flint.
Other descriptions in use are uneven, splintery, hackly and earthy. They are less diagnostic than cleavage but still worth recording.
Telling them apart
Cleavage surfaces are flat, reflective, and repeat in parallel sets across a specimen. Fracture surfaces are irregular and do not repeat.
A single flat face proves nothing on its own — it may be a growth face. Look for the repetition.
Recording what you see
Cleavage is described by quality and by the number of directions: perfect, good or poor, in one, two, three or more directions, with the angles between them where those can be judged.
Calcite shows perfect cleavage in three directions that are not at right angles, which is why the fragments are rhombs. Galena shows perfect cleavage in three directions that are at right angles, which is why its fragments are cubes. Noting the angle is what separates the two descriptions.