Now checking my android phone, main screen just there on the top ... oh hey google in a multicolor G ...
yes they both qualify as adaware. The difference seems that the Apple approach is at least context-aware. You don't get random ads or suggestions system-wide. You get ... newspaper ads in the newspaper app, or music ads in the music app.
I honestly wish we had the same on the android front. Google is decidedly much more invasive these days