elliptical sentence definition

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.