I found you!!!
This is Tim! Thanks for doing all this!
I can see how much you want to know about this! That's great to know!!!
Okay, let's take a look at your question... Shall we?
you wrote, 공부하다 [gong-bu hada] "to study"
공부해 [gongbuhae] "study"
미안하다 [mianhada]
미안해 [mianhae]
What is actually the difference between “hada” and “hae”?
Okay! First, let's compare those with English words.
공부 [gongbu] is a noun that means "study". It's a NOUN!
공부하다 [gongbuhada] is a verb that means "to study". It's a VERB! - 'standard form'.
Note! in English, "study" can be meant for both a noun and a verb.
and 공부해 [gongbuhae] is a verb that basically means the same as "to study" - 'casual speech'.
Remember this! - the beauty of learning Korean is to learn about the CONJUGATION rules. (there are many)
For example #1,
Standard - 하다 [hada] "to do" i.e) I do my homework. 나는 숙제를 하다. (we don't say it like this!)
Casual (informal) speech - 해 [hae] "to do" i.e) I do my homework. 나는 숙제를 해 (talking to someone younger than you or to your friends)
To make and sound it (above) politer, you add 요 right after 해; so it becomes 해 + 요 => 해요. 나는 숙제를 해요 (politer)
Formal speech - 하 +ㅂ니다 = 합니다 [hapnida] "to do" i.e) I do my homework. 저는 숙제를 합니다. (나 => 저 & 하다 => 합니다).
now you see the difference? it's all about who are you talking to?
For example #2,
Standard - 공부하다 [gongbuhada] "to study" i.e) I study Korean. 나는 한국어를 공부하다. (we don't say it like this!)
Informal speech - 공부해 [gongbuhae] "to study" i.e) I study Korean. 나는 한국어를 공부해 (to the younger or friends)
To make and sound it (above) politer, you add 요 right after 해; so it becomes 공부해 + 요 => 공부해요. 나는 한국어를 공부해요 (politer)
Formal speech - 공부하 + ㅂ니다 = 공부합니다 [gongbuhapnida] "to study" 저는 한국어를 공부해요 (나=>저 & 공부하다 => 공부합니다).
For example #3,
standard - 미한하다 [mianhada] "to feel sorry" i.e) I am sorry. 미안하다 (we don't say it like this!!)
Informal speech - 미안해 [mianhae] "to feel sorry" i.e) I am sorry. 미안해 (to the younger or to your friends)
To make it politer, add 요 right after 해; so it becomes 미안해 + 요 => 미안해요 (politer).
Formal speech - 미안하 + ㅂ니다 =미안합니다 [mianhapnida] "to feel sorry" 미안합니다 (미안하다 => 미안합니다).
and keeps going...
I hope my explanation is easy and very comprehensible for you...
cheers,
Tim
