A treasury is either
The head of a treasury is typically known as a treasurer. This position may not necessarily have the final control over the actions of the treasury, particularly if they are not an elected representative.
The adjective for a treasury is normally treasurial. The adjective "tresorial" can also be used, but this normally means pertaining to a treasurer.
...And there was also silver weighing many thousands of talents and all the royal treasure amounting to a very great sum...
The term treasury was first used in Classical times to describe the votive buildings erected to house gifts to the gods, such as the Siphnian Treasury in Delphi or many similar buildings erected in Olympia, Greece by competing city-states to impress others during the ancient Olympic Games. In Ancient Greece treasuries were almost always physically incorporated within religious buildings such as temples, thus making state funds sacrosanct and adding moral constraints to the penal ones to those who would have access to these funds.
The sovereigns' treasury within the palace in ancient Jerusalem, is considered to be similar in nature to the temple treasury. The temple treasury of the settlement had appointed officials and functioned akin to a bank.
... in fact, practically in every city there are banking places for the holy money ...
In excavations of Persepolis a text containing information pertaining to the activities of a temple treasury were discovered dated to the fifth century BC. The texts written in the Elamite language name the treasurer as ganzabara 
In the United Kingdom, Her Majesty's Treasury is overseen by the Chancellor of the Exchequer. The traditional honorary title of First Lord of the Treasury is held by the Prime Minister. Her Majesty's Revenue and Customs administers the taxation system.
In many other countries, the treasury is called the "ministry of finance" and the head is known as the finance minister. Examples include the Bahamas, Bangladesh, Belgium, Spain, Italy, New Zealand, Ghana, Canada, Malaysia, Singapore, India, Japan, the Netherlands, Pakistan and Zimbabwe.
In some other countries, a "Treasury" will exist alongside a separate "Ministry of Finance", with divided functions.
The State Treasury (Polish: Skarb Pa?stwa) in Polish law represents the Polish state acting in the field of civil law relations in which it is treated as equal partner to private entities (as opposed to the sphere of public law relations in which the State represented by public authorities decides unilaterally on the legal situation of individuals). It can be represented by various officials or institutions depending on circumstances and has its own ministry, the Ministry of State Treasury. Historically, it was created in the Crown of the Kingdom of Poland in 1590, when the public treasury (or the Crown Treasury) was split from the Royal Treasury.
In the Australian federal government a treasurer and a finance minister co-exist. The Department of the Treasury is responsible for drafting the government budget, economic policy (except monetary policy), some market regulation and revenue policy (which is administered by the Australian Taxation Office). The Finance Minister, who manages the Department of Finance and Deregulation, is responsible for budget management, government expenditure and market deregulation.