We analyze the dynamics and activity observed in bodies approaching the Earth (perihelion distances q < 1.3 au) in short-period orbits (P < 20 yr), which essentially are near-Earth Jupiter Family Comets (NEJFCs) and near-Earth asteroids (NEAs). In the general definition, comets are “active”, i.e. they show some coma, while asteroids are “inactive”, i.e. they only show a bare nucleus. Besides their activity, NEJFCs are distinguished from NEAs by their dynamical evolution: NEJFCs move on unstable orbits subject to frequent close encounters with Jupiter, whereas NEA orbits are much more stable and tend to avoid close encounters with Jupiter. However, some JFCs are found to move on stable, asteroidal-type orbits, so the question arises if these objects are asteroids that have become active, perhaps upon approach to the Sun. In this sense they may be regarded as the counterparts of the main-belt comets (Hsieh & Jewitt 2006). On the other hand, some seemingly inert NEAs move on unstable, comet-type orbits, so the question about what is a comet and what is an asteroid has become increasingly complex.