Escapement

A mechanism that is fitted between the gears and the regulating organ. Its function is to suspend the gears' motion at regular intervals and to supply energy to the balance.

recoil escapements (verge or crown wheel)
dead-beat escapements (cylinder, virgule, double virgule)
detached escapements (lever, detent)

The lever escapement is by far the most common today. Exceptional watches may be fitted with a different kind, often a detent or virgule escapement.
In terms of escapements, one can historically speak of the lever and indeed the Swiss lever type, given that the Swiss lever escapement is the most widely used today because it is especially suited to watches and chronometers.