Is it ok to call BIP39 supporting wallet also a HD wallet (Hierarchical Deterministic Wallet) or does it refer to something else?
Yes, but they are not synonymous.
HD wallets are any wallets which produce keys in a deterministic fashion.
BIP39 describes the implementation of using a series of words as the seed to this deterministic process.
So all BIP39 wallets are HD wallets, but not all HD wallets are BIP39 wallets. Bitcoin Core, as the most notable example, is HD but does not use BIP39 seed phrases.