Some people would consider saying "oh my God" as blaspheme, "oh my gosh" can be seen as a softer version of the same thing. I happen to know a few others: "shit" (bad) ==> "shoot" (not as bad) "damn" (bad) ==> "darn" (not as bad)

In the Jewish tradition (and later in the Catholic tradition) it was forbidden to pronounce God's name. Since there is a commandment that says that the name of God should not be pronounced in vain. Since the pronunciation of God's name was lost, they decided that it was also offensive to say the word "God" as an exclamation. So, in order to avoid saying the word "God" in the exclamation "oh my God!" they say "oh my Gosh!", which is basically the same when they change a letter in other expressions to make the sound nicer. For example "hell" for "heck", "holly shit" for "holly cow", "this fucking job" for "this f-ing job", and so on.

Nothing at all, some people just prefer to say one over the other. They are the same.

As people said before, Oh my gosh and Oh my God have the same meaning. You could say that the Korean equivalent is Aigoo. Although Oh my God has in the past been considered a more offensive version, recently, it is becoming less offensive in nature. Many people also say "OMG" or "Ohemgee" as a slang version of it.

The meanings are not the same. Gosh is a nonsense word, a "gonzoism". God refers to Deity. In order to avoid giving offense to "God" somebody decided to employ gonzoism, instead.