Difference between not waking up to the alarm and missing the alarm

Hi teachers~

I would like to make sure if I understand the difference between not waking up to the alarm and missing the alarm.

"I didn't wake up to my alarm."-meaning I didn't hear the alarm.

"I missed my alarm." meaning either I didn't hear the alarm or my alarm might have gone off but for some reason it didn't ring.

Are both expressions the most common?

Thank you~~