Learn English – Why is ‘unexpectedly’ common but ‘expectedly’ not

The use of "Korea" to mean "South Korea" is far more common in the adjectival form. E.g. "Korean automaker", "Korean pop music" or "Korean soap opera".

Owing to North Korea's status as an economical, cultural, and political walled garden - or perhaps it's more apt to say "walled mudflat" - there are very few words to which the adjective "Korean" commonly applies for outsiders. "Dictator", of course, is the obvious exception.

Thanks largely to the media, this adjectival shorthand usage is firmly entrenched.

In nounal form, my sense is that the mapping is much further from one-to-one. (Since I don't know how to search one of these online corpuses for "this when not neighbored by that", I can't confirm that anecdotal evidence with data, alas.)

While "Korea" would be formally correct within their own language since they are formally the Republic of Korea, in English the pattern of usage I observe is to at the very least differentiate them on first usage.

For example, this is a pattern I hear often in the financial news: "Korean automaker Kia announced today it will be bringing 50,000 new jobs to South Korea. The company has long dominated the auto market in Korea and is now seeking..."

First nounal mention: South Korea. Subsequent mentions can be simply Korea.

So I'd lean toward not linking the tag Korea to South Korea exclusively.

In my experinece you run into people and trouble:

I ran into Betty at the store today. I haven't seen her since college!
I ran into your co-worker Bob today.
Sorry I'm late; I ran into heavy traffic.

You come across objects:

I was cleaning up the kitchen and came across that phone bill you lost.
I was looking up (something) in the encylopedia and came across this interesting tidbit.

I'm not sure I'd use either when talking about a grammar error in a blog; I'd be more likely to say I found or noticed it. I don't know why that is.