With examples from Terminator: The Sarah Connor Chronicles
Despite the similarity in these words, they really do have two different meanings.
According to Dictionary.com, crush is a verb that means "to press or squeeze with a force that destroys or deforms; to squeeze or pound into small fragments or particles; and even to hug or embrace forcibly or strongly."
Cameron watched as the tractor trailer flipped over, its wheels spinning in space, while sparks flew from the rig as it skid along the pavement. The crushed cyborg rose up from the ground, its silver chassis gleaming under the street lights.
They had survived the battle somehow. Sarah stared at her son for a moment, then pulled him close to crush him in an embrace. His survival was more important than anything.
Another common use for crush is the slang definition - "an intense but usually short-lived infatuation."
John could tell that the girl sitting next to him in class had a major crush on him. He just chose to ignore it. The way his life was going, he wouldn’t be in this classroom for too long anyway.
It wasn’t just a crush, Cara thought as she stared at John Connor, who sat next to her in class. Her feelings ran deep, deeper than she could ever imagine.
Crash, on the other hand, means "to make a loud, clattering noise, as of something dashed to pieces; or to land in an abnormal manner, usually causing severe damage."
The loud crash coming from John’s room scared Sarah into action. She ran to his bedroom, threw open the door and stared in dazed confusion at the overturned chair and the smile on her son’s face. "What happened?" she demanded, her heart still racing with the fears that ran through her thoughts.
Derek swerved violently to the right, desperately trying to avoid hitting the bus. He slowed only slightly, then sped up again to stay ahead of the machine that was chasing him. He tried not to think about casualties as he drove away from the sound of twisting metal and splintered glass, knowing full well that the people in that bus would be lucky if they survived the crash.
Crash also can mean, "to collapse or fail suddenly, as a financial enterprise; and to fall asleep; or shut down because of a malfunction of hardware or software."
After a long day of running from the machines, John flopped down on the bed for some much-needed sleep. "I just need to crash here for a while," he told Cameron. "A few hours, that’s all."
"The CPU is fried," John said with a frustrated sigh. "I should have known it was on its way out. I just didn’t expect it to crash so soon."
One possible way to remember which word to use is think of the results. If something breaks into pieces or produces a loud noise, use crash. If something is flattened but doesn’t break apart, use crush.