You've got your Aldis mixed up. Aldi Nord owns Trader Joe's (not the other way around). Aldi stores in the US are Aldi Süd. The two are separate companies, Aldi Nord serves the North of Germany and Aldi Süd the South. Their international expansions are separate as well. Here's a handy map (Aldi Nord in blue): https://upload.wikimedia.org/wikipedia/commons/6/67/Aldi_wor...

The line dividing Germany into Aldi Nord and Aldi Süd territory — https://upload.wikimedia.org/wikipedia/commons/f/fc/Aldi_equ... — is called the "Aldi equator". We sometimes jokingly call it Germany's most important dividing line post-reunification :)

tl;dr Aldi and Trader Joe's are (theoretically) in competition, and neither owns the other. The other Aldi owns Trader Joe's.