What exactly counts as a false start?

Under World Athletics TR 16.7, once in their full and final starting position, an athlete may not begin their start before the gun. The start begins:

• Crouch start: any motion that includes or results in one or both feet losing contact with the foot plates, or one or both hands losing contact with the ground.
• Standing start: any motion that results in one or both feet losing contact with the ground.

It's also a false start if an athlete starts a movement before the gun that doesn't stop and carries on into the start (a "rolling start").

Not false starts:

• Other movements, such as raising the hips and lowering them again without hands or feet losing contact. These may be dealt with as improper conduct instead.
• In standing starts, an accidental overbalance can be treated as an "unsteady" start rather than a false start. An athlete pushed or jostled over the line shouldn't be penalised; the athlete who caused it may be warned or disqualified.

World Athletics guidance asks starters and referees not to be over-zealous with standing starts.