When to use: 어머지 vs. 엄머 하고 아버지 vs. 아빠
I've been studying 한국어 using the Living Language 한국어 edition books, and just learned about 가족 members. The one that I wanted to ask about is how to call your mom or dad in Korean. The book teaches you to call mother 어머니 and father is 아버지.

But, when watching a Korean drama, I heard a character say 엄마/아빠. Does the latter mean mom/dad (as opposed to mother/father)? Or do these words denote a level of respect (much like the Japanese kaasan 母さん、hahaue 母上?)?

I would like to know because I've switched my phone language to Korean and wanted to change some contact labels also.

Question

When to use: 어머지 vs. 엄머 하고 아버지 vs. 아빠
I've been studying 한국어 using the Living Language 한국어 edition books, and just learned about 가족 members. The one that I wanted to ask about is how to call your mom or dad in Korean.  The book teaches you to call mother 어머니 and father is 아버지.

But, when watching a Korean drama, I heard a character say 엄마/아빠.  Does the latter mean mom/dad (as opposed to mother/father)?  Or do these words denote a level of respect (much like the Japanese kaasan 母さん、hahaue 母上?)?

I would like to know because I've switched my phone language to Korean and wanted to change some contact labels also.

Answer

Yes, something like that.:)
"엄마" and "아빠" can mean "mom" and "papa" respectively.
They sound sweet and friendly, often are used in casual conversations.
"아버지" and "어머니" are formal versions of "아빠" and "엄마".

When someone calls their parents "엄마" or "아빠", it doesn't mean they don't respect their parents.:)

\^o^/

Answer

"A level of respect"

That's right.
but think simply

엄마, 아빠 is informal. It sounds more familiar. I also usually say 엄마 엄마~. 
but actually it's for kids. as we grow older, we change some words, just like from 엄마 to 어머니

if you're an adult and you say 엄마 in front of other elder person, he/she thinks you're immature.

I also use 엄마 when I'm home but if there are some other people(especially my mother's friends) around us, I say 어머니.
because I also think if someone calls her/his mother as 엄마, she/he is immature.
Using 어머니 depends on home atmosphere and home education but we should keep them.