Is Trader Joe Aldi?

I'm curious to know if Trader Joe's and Aldi are one and the same company. Both of them are known for their low prices and wide selection of grocery items, but I've never seen them explicitly linked as being part of the same brand. Could you please clarify if Trader Joe's and Aldi are in fact the same entity, or are they separate companies with similar business models? It would be helpful to understand the distinction, if any, between the two.