A union may be effected in a number of forms, broadly categorized as:
In an incorporating union a new state is created, the former states being entirely dissolved into the new state (albeit that some aspects may be preserved; see below "Preservation of interests").
Nevertheless a full incorporating union may preserve the laws and institutions of the former states, as happened in the creating of the United Kingdom. This may be simply a matter of practice or to comply with a guarantee given in the terms of the union. For example:
In an incorporating annexation a state or states is united to and dissolved in an existing state, whose legal existence continues.
Annexation may be voluntary (as with Montenegro's union into Serbia in 1918) or, which is more frequent, by conquest.
In a federal or confederal union the states continue in existence but place themselves under a new federal authority. The federal state alone will be the state in international law though the federated states retain an existence in domestic law.
If a state becomes a federated unit of another existing state, the latter continuing its legal existence, then that is a federal annexation. The new federated state thus ceases to be a state in international law but retains its legal existence in domestic law, subsidiary to the federal authority.
(Arguably Hawaii with the United States of America is an example, but Hawaii was first annexed without statehood.)
The unification of Italy involved a mixture of unions. The kingdom consolidated around the Kingdom of Sardinia. Several states voluntarily united with Sardina to create the Kingdom of Italy. Others, the Kingdom of the Two Sicilies and the Papal States were conquered and annexed.
The unification of Germany was ultimately a confederal union, but it began in earnest by Prussia's annexation of numerous petty states in 1866.
Lord Durham was widely regarded as one of the most important thinkers in the history of the British Empire's constitutional evolution. He articulated clearly the difference between a full legislative union and a federation. In his 1839 Report, in discussing the proposed union of Upper and Lower Canada, he says:
Two kinds of union have been proposed – federal and legislative. By the first, the separate legislature of each province would be preserved in its present form and retain almost all its present attributes of internal legislation, the federal legislature exercising no power save in those matters which may have been expressly ceded to it by the constituent provinces. A legislative union would imply a complete incorporation of the provinces included in it under one legislature, exercising universal and sole legislative authority over all of them in exactly the same manner as the Parliament legislates alone for the whole of the British Isles.