In Germany, they are not just owned by the same group, it's the exact same company ("Deutsche Post AG", the parent company of the group) and you talk to the exact same persons to use their services. Letters and small packages use the "Deutsche Post" brand and larger ones use "DHL" but that should not be confused with the DHL you find in the US. Despite the name they are still the USPS of Germany. They differentiate because in larger cities they deliver both services separately, i.e. your Amazon order will not be delivered with your letters in the morning but later in the day. They also have a US-style service which they call "DHL Express".

You can choose to have your package delivered by DHL US instead of USPS but that is not the default option when shipping from Germany. You have to through DHL Express for that.

All of the large US couriers have a service where they use USPS for the last mile: DHL eCommerce, UPS SurePost, FedEx SmartPost.