A Domestication is the transfer of the domicile of incorporation of a company from a jurisdiction of origin to another (new) Domestic jurisdiction of destination. All assets & liabilities are transferred in one single process. In some jurisdictions, the Domestication includes the transfer of the starting date of incorporation; in others, the company is given a new birth date.
A Continuance however, is a Domestication which guarantees the lifetime of company since birth, thus the company retains its age. The company just moves and continues its life in the new jurisdiction.
In both cases, prior to any Domestication or Continuance, the company must be authorized by its shareholders/members in the old jurisdiction of origin to do so, and then (ideally) dissolved once the move has been completed.
Other names are also given to this process: Corporate Migration, Migration of Company, Redomiciliation, Transfer of Domicile, or Redomicile.
Do not think that this is something unusual: big companies listed on Stock Exchanges do this, for example Teekay Shipping Corporation (listed on the NYSE), which moved from Liberia to the Marshall Islands in 1999.
Today it is very cheap to complete the process of a Continuance to Wyoming. We offer such services without an expensive lawyer, and takes up to 3 months to complete.