No, there are regular Corollas with E120 and E130 codes. I thought it was a question of size (smaller JDM versus bigger export versions), but it could be instead related to differences in drivetrain or even suspension systems (that's to be confirmed).

Anyway, I'd prefer keeping US-spec Corollas with those ZZE130 or 131 codes... because it's just those two codes. That makes it easier to distinguish US-spec Corollas from the whole bunch of "E120 by default" Corollas we have on the site.

And just keep E130 for the Matrix, without any "ZZ", because the choice isn't as simple as for Corolla sedans.

http://www.toyotareference.com/matrix/2003-2008