Check on sth and check up on sth

Hi teachers~

I mistakenly posted the same question without logging in, so I posted again.

Would you tell me the difference between 'check on sth' and 'check up on sth?'

CHECK ON STH: to https://www.ldoceonline.com/ko/dictionary/try to find out if something is https://www.ldoceonline.com/ko/dictionary/true or https://www.ldoceonline.com/ko/dictionary/correct

Ex) He wanted to check on the girl’s story.

CHECK UP ON STH: to make https://www.ldoceonline.com/ko/dictionary/sure that something is or

Ex) Dustin called me to check up on some facts.

Thanks in advance.