Number of addresses on a cold hardware wallet?

[lunarlanding2021]

If using one of the major brand cold storage hardware wallets to store BTC, does the hardware wallet have one unique address or can it store many different BTC addresses so that purchased BTC could possibly be stored across many different BTC addresses stored on the same cold storage hardware wallet?

[hosseinimr93]

Hardware wallets like Ledger and Trezor provide a HD (Hierarchical Deterministic) wallet for you.
A HD wallet gives you numerous addresses and private keys that are all generated by a seed phrase (a series of words) and you can use a new address every time you receive bitcoin.

[lunarlanding2021]

Hardware wallets like Ledger and Trezor provide a HD (Hierarchical Deterministic) wallet for you.
A HD wallet gives you numerous addresses and private keys that are all generated by a seed phrase (a series of words) and you can use a new address every time you receive bitcoin.

Thank you.

[bitmover]

Hardware wallets like Ledger and Trezor provide a HD (Hierarchical Deterministic) wallet for you.
A HD wallet gives you numerous addresses and private keys that are all generated by a seed phrase (a series of words) and you can use a new address every time you receive bitcoin.

Exactly.

When you setup a hardware wallet, the only thing you have to worry about is storing your seed (24 words which you note down in a piece of paper) safetly.
The seed is all you need to recover your funds.

From your seed, you can derive billions of addresses. You can generate an address any time you like for free.

Deterministic (Seeded) Wallets
Deterministic, or “seeded” wallets are wallets that contain private keys that are all derived from a common seed, through the use of a one-way hash function. The seed is a randomly generated number that is combined with other data, such as an index number or “chain code” (see Hierarchical Deterministic Wallets (BIP0032/BIP0044)) to derive the private keys. In a deterministic wallet, the seed is sufficient to recover all the derived keys, and therefore a single backup at creation time is sufficient. The seed is also sufficient for a wallet export or import, allowing for easy migration of all the user’s keys between different wallet implementations.

https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch04.html

[dkbit98]

If using one of the major brand cold storage hardware wallets to store BTC, does the hardware wallet have one unique address or can it store many different BTC addresses so that purchased BTC could possibly be stored across many different BTC addresses stored on the same cold storage hardware wallet?

You can create as many addresses as you want and not only that but you can also create many bitcoin accounts with different address formats, like old legacy format starting with number 1 or newer formats starting with 3 and bc1.
Important thing is to add this information like wallet you used, address format and derivation path to your seed words backup, so you can recover it easier in future.