There are two ways of dealing with glyphs that share code points. The first is TTC (truetype collection) fonts. A TTC is basically one set of glyphs with several sets of mappings (i.e. which code point maps to which glyph). When you install it, assuming your computer groks ttc, your system shows you a separate font for each mapping. Taking for example Source Han Sans, which adobe just released - if you go to the download page[0] and get the complete version (the "OTC" one), you get a bunch of files like "SourceHanSans-Bold.ttc". If you install one of them you'll see four new fonts: "Source Han Sans J", K, SC, and TC. Then when you use the font, depending on which font name you used the system will change which mapping it applies to the combined set of glyphs. (Hence the choice of font name is the selection mechanism you described.)

The second way is that TrueType fonts have a way to build locale settings into the font. I'm less clear on the details here but apparently it's similar to TTC behind the scenes, except that the mappings are associated with locales - so in an app that supports TT locales, even if you select "Foo J" as your font, when the locale was simplified Chinese you'd get the SC glyph. Of course now the selection mechanism is whether the application knows what locale the content is. (And also whether it supports the mechanism - I don't know how widespread this is.) Either way though, in principle you get different glyphs for the same code point, depending on context.

Or anyway that's the understanding I took away as a font layperson - happy to be corrected.

[0] http://sourceforge.net/projects/source-han-sans.adobe/files/