9 years later but should be useful for others:

The Garmin units sold in Europe and North America DO NOT support Oriental maps.

You must buy a DIFFERENT hand set for Japan and a DIFFERENT handset for Korea. It may be possible to fit Korean on the Japanese model or Japanese on the Korean model but it would not be a trivial exercise. You certainly CANNOT do the same with European models as the internal memory on the Garmin is too small to support the double-byte character set.

So, for Korea, you should just download Naver Maps on your smartphone if you want to go to the mountains. If you are not interested in the mountains either Daum or Naver will do.

The Open street Maps may suffice for a holiday but they are really so far behind the pace of construction in South Korea that they are otherwise not worth considering.

I do not understand why OSM maps will not work.

I had maps from Japan in just for testing reasons and I did use OSM maps from Turkey to Mongolia and Russia in a Garmin device.
And it always worked.

In fact, I consider OSM maps as very good actually.

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www.klausmotorreise.com

I do believe Garmin GPS units are sold around the world .. and that there are no specific GPS units for any country/area.
Some GPS units have maps installed for the country they are sold in .. that does not mean the GPS itself is specific to the country, just the map!

The OSM maps from Free worldwide Garmin maps from OpenStreetMap show things in English .. which is handy for visitors who are more familiar with English particularly where local signs show English names as well as the local language (like South Korea).

International character support (sandscript, Kanji, etc) I have no knowledge of .. so I will not comment. But at least some Garmin GPSes use a microSD card .. the amount of memory is not a problem for these, implementation of international character support might be a problem.

Most maps suffer from new stuff coming along. Keeping OSM upto date relies on the local community and the infrequent visitor, and OSM is fairly good in keeping upto date where there are locals prepared to help.

Other than OSM .. amazon offers https://www.amazon.com/Japan-Korea-2.../dp/B01F1EOR7Q Note: this is in English too... and may not have more detail nor be more current than OSM.

Add.........

http://admincabal.com/osm/ has an OSM Japan map in kanji and kana. Dated 2012 for PC installer, .imj file is july 2015 (more upto date).

Nerds interested in international character support may look at http://wiki.openstreetmap.org/wiki/Mkgmap/i18n

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To answer the original questions

1 Garmin map or OSM ... Garmin City Nav not available to 'us', other sources may not be that much different from OSM. I'd go with OSM. If a ginuine Garmin map were available .. it would probably have more detail, more POI .. these may not be of much value to a casual tourist.

2 Languages .. as stated above signs carry both the local language and English, so an English OSM map should not be too much of a problem. As time goes on 'we' might get GPS maps that can be switched from one language to another ... would certainly help tourists!