Most people just call it Mid-City since the area is the middle of the city and extends quite far from Wilshire.
Anyhow, Mid-Wilshire refers to that busy, urban swath between Downtown and Beverly Hills, kept in check by mountains to the north the the 10 Freeway to the south (though immediately above the 10 Freeway, like the areas far below it, are neighborhoods too poor and residential to fit the mental image conjured by Mid-Wilshire.)
Including Koreatown, with Grand Spa. Apparently there is a Little Bangladesh here, a largely invisible district except on Bengali Independence Day when turning off sleepy Westmoreland will find you in the middle of a a carnival on 7th Avenue, complete with an enormous ferris wheel and other roller coasters (seemingly appeared out of nowhere).
Hancock Park Fairfax District
This could include LACMA, The Grove, not much south (boring, residential) and east of LaBrea the buildings get low, office-oriented -- an incredibly dull area until Koreatown livens things up around Western. It has Hollywood's nutty flavor, but without the fruitiness: amid old restaurants and a used prop store, is an Orthodox neighborhood; quiet family homes; and other trappings indistinguishable from SFV except for the nearby din and older, prettier buildings.