HDFC and HDFC Bank are two different entities. HDFC Bank is an offshoot of the much older parent organization that's HDFC. They have different executive managements.
I am a customer of both. I fell very happy about HDFC while extremely unhappy about HDFC Bank!
The staff of HDFC and HDFC Bank are a world apart. The former has the best and most knowledgeable staff, whereas the latter just sucks in that department!