Tweakable encryption algorithms vs Key wrapping I have read many articles about Key wrapping and tweakable cipher modes.
However, I don't understand the main difference between them?
What you recommend for Key storage and Key Archive.
Key wrapping and tweakable encryption are actually quite different topics.
Key wrapping is more commonly related to keys forage and key archive.

Key wrapping

This is fancy terminology for encryption key with another key. 
In key wrapping you have a master key that is used to protect one or more keys. It is generally impossible for (computationally constrained adversary) to decrypt wrapped key with no access to appropriate decryption key.

There are key wrapping mechanisms used with asymmetric cryptography, i.e. encryption and decryption with different key (such as RSA-OAEP), and symmetric cryptography, such as AES-KW. Many key wrapping algorithms provide some level of integrity/authenticity protection in addition to encryption.

For purposes of key storage and key archive, key wrapping is very often used.

Key derivation

(As introduction towards tweakable encryption). Key derivation is kind of counterpart of key wrapping. The master key is not used to protect wrapped key, but instead a key derivation algorithm is used to produce other keys from master key. The algorithm may, for instance, generate the keys based on purpose (as identified by "Label") and possibly, other fields related to context. Key derivation can be useful when many keys are needed, but it is not desirable to store all the keys, but only store the master key. (Thus, for key storage, this algorithm is not ideal.)

Tweakable encryption

In some fields, most notably Full Disk Encryption, it is would be desirable to use very large number of cryptographic keys, for instance, to use different cryptographic key per each sector. Conceptually, this is very close to using key derivation to derive per sector keys. Unlike key wrapping, in tweakable encryption the per sector keys are not (usually) stored anywhere.

The tweakable encryption algorithms have been usually implemented with optimization goal that it is very lightweight to change one parameter (tweak).
For purpose of key storage and key archive, in many cases, current tweakable encryption algorithms are of little use. Tweakable encryption (for instance XTS-AES), is mainly intended to protect (lower value) bulk data, in situations where data size extension to allow for integrity/authenticity checking is not an option.