Transit visa at Helsinki airport

First of all, to answer your question: No, you cannot get a transit visa; to do what you are asking about, you need a regular Schengen short-stay visa.

(There are exceptions, of course, a detailed account of which is beyond the scope of this question. This answer assumes that you are a national of a country whose citizens require a visa to enter the Schengen area, and that you do not have another document that authorizes entry in lieu of a short-term visa.)

The general point is that to leave the airport, or indeed to pass through immigration for any length of time, you must meet the same entry requirements as someone seeking a short visit under the 90/180 day rule. That is to say, there is no such thing as a "transit visa" in the Schengen visa code.

There used to be such a thing, however. The original Schengen visa scheme comprised four types of visa. Some internet sites continue to describe this obsolete scheme:

• A: Airport transit visa: Required of nationals of a small number of countries for transit while remaining within the international zone of an airport. That is, this visa allows people to change planes in the airport, but does not allow them to pass through immigration. Most countries' nationals are exempt from this requirement.

• B: Transit visa: Required of most countries' nationals for transit of up to five days in the Schengen area while traveling from one non-Schengen country to another.

• C: Short-term visa: Required of most countries' nationals for visits in the Schengen area of no more than 90 days in any 180-day period.

• D: Long-term visa (also called national visa): Required of nationals of all non-EU countries who wish to remain in a Schengen country for more than 90 days.

(Source: http://www.schengenvisainfo.com/schengen-visa-types/)

The 2009 version of the Schengen visa code, which took effect in 2010, abolished the transit visa. Its definition of visa is (emphasis added):

2. ‘visa’ means an authorisation issued by a Member State with a view to:

   (a) transit through or an intended stay in the territory of the Member States of a duration of no more than three months in any six-month period from the date of first entry in the territory of the Member States;

   (b) transit through the international transit areas of airports of the Member States;

The visa type letters are not mentioned in the main body of the legislation, but the remaining type designations -- A, C, and D -- are specified in Annex VII:

7. ‘TYPE OF VISA’ heading:

In order to facilitate matters for the control authorities, this heading specifies the type of visa using the letters A, C and D as follows:

A: airport transit visa (as defined in Article 2(5) of this Regulation)

C: visa (as defined in Article 2(2) of this Regulation)

D: long-stay visa

(Source: http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:02009R0810-20131018)