"Sleep Like a Baby" vs. "Cat Nap"

The term, "sleep like a baby" doesn't make much sense to us. We use it to mean we slept really, really well. Conked out. Zzzz. But every baby we know sleeps through loud things like car alarms and construction vehicles, while starting awake when someone walks past his or her room. Shouldn't we use the term to mean we slept through an earthquake but woke up when someone sneezed?

We've encountered a very curious phenomenon in our house. Owen cat naps and our cats sleep like babies. Owen takes short 30 minutes naps throughout the day, and Purna sleeps under the bed for 5, 6, 7 hours at a time. Hmm.