elliptical sentences are sentences in which part of their structure has been omitted (Latin ellipsis:"falling short").
A:Where are you going?
B:[I'm going] to Greymouth.***
A:When are you leaving?
B:[I'm leaving] early tomorrow morning.***
They are not the same as incomplete sentences.
"I hope that you ..." Sidney choked and stopped.
"I can tell you who the murderer is!Look at the ..."
A shot rang out,and she slumped to the floor.