• (-에) 관 - relating, affiliating (with)
(-에) 대 - facing, focusing (on)
Difference lies in the focus,
관 -> emphasis on the action taken relating to some issue
대 -> focus on a specific issue
• (-에) 관하다 - be about
(-에) 대하다 - be on, in, of
• (-에) 관한 [N] - Lit. been (being) about [N] (-에) 대한 [N] - Lit. been (being) on [N]
used as adjectives modifying the noun/nominalized phrase [N]
• (-에) 관하여 / (-에) 대하여 [V], Formal form of (-에) 관해(서) / (-에) 대해(서) -
[해 is the collapsed version of 하여]
(-에) 관하여 [V] ~ [V] about
(-에) 대하여 [V] ~ [V] of/in/on
used mainly as postpositions (Eng. prepositions) to modify the following verbs or phrasal verbs [V].
Apologies for the confusion. Not easy to explain the difference between "관-" vs "대-" I must admit.
From what I understand, the affix "관-" (noun) in this case, means "matters concerning".
"대-" is a bit more difficult to explain. 대 as a preposition is akin to "re." (= with regard to) or "vs." (= against) in English. The affix "대-" stands for "matters regarding".
The difference between "관-" & "대-" is much like that between "concerning" and "regarding". In common usage, it is negligible. That explains why ~에 관한 & ~에 대한 can be used interchangeably.
관한 vs 관하여
(1) 관한 is the adjective form of 관하다. It serves to modify/describe a Noun. So 관한 will always go before a Noun.
한국 풍습에 "관한 책" = "book which are related to" Korean customs = book about Korean customs.
문화에 관한 잡지 = magazine which is related to culture = magazine about culture
(2) 관하여 [ / 관해서 / 관해 ] is a phrasal adverb. It describes/modifies an action (i.e. a verb). So 관하여 will always go before a Verb.
한국 관습에 관하여 이야기하다 = Speak on the subject of / about Korean customs
문화에 관하여 쓰다 = write on the subject of/ about culture