Let’s learn the meanings of terms.
Deterministic means that keys are no longer created randomly, but instead generated as part of a linked chain. Regular backups are no longer required as long as the private-key seed that created the chain is safe. This makes key management very simple, and even allows easy caching of the master key in a paper wallet or cold storage--only having child keys stored on more vulnerable computer hardware.
Hierarchical means that the chain of keys is ranked so that lower-rank keys cannot reveal information about their higher-ranked brethren. This also allows the selective sharing of public keys for auditing purposes.
Deterministic wallets were developed to make it easy to derive many keys from a single seed.
HD wallets contain keys derived in a tree structure, such that a parent key can derive a sequence of child keys, each of which can derive a sequence of grandchild keys, and so on.
HD wallets offer a few key advantages over simpler deterministic wallets. First, the tree structure can be used to express additional organizational meaning, such as when a specific branch of subkeys is used to receive incoming payments and a different branch is used to receive change from outgoing payments. Branches of keys can also be used in corporate settings, allocating different branches to departments, subsidiaries, specific functions, or accounting categories.
The second advantage of HD wallets is that users can create a sequence of public keys without having access to the corresponding private keys. This allows HD wallets to be used on an insecure server or in a watch-only or receive-only capacity, where the wallet doesn’t have private keys that can spend the funds.