They are not the same company in the US. Trader Joe’s is owned by Aldi Nord, which does not operate any Aldi stores in the US.
Aldi Nord and Aldi Süd only compete in Germany with those respective names, and the United States with Trader Joe’s and Aldi respectively. They essentially divided up the rest of Europe and do not compete with each other.
So the Aldi in the United States is not the same company as Trader Joe’s.