The first thing to note is that the county as an administrative unit is not indigenous to Wales, rather Wales was a country of commotes and cantrefs, and the county was an English concept imposed on Wales as a result of military conquest.
From 1284 to 1536
It was the Statute of Rhuddlan in 1284 that first introduced the English concept of the county into Wales, dividing the former Welsh kingdom or principality of Gwynedd into the counties of Anglesey, Caernarfon and Merioneth. A similar development occurred in the royal territories of Cardigan and Carmarthen; in the north east the district of Flint (under the aegis of the palatinate of Chester) became a proto-county and something akin to a feudal county developed in both the territories of Glamorgan and Pembroke.
From 1536 to 1974
It was the Acts of Union 1536-1543 that brought about the Shiring of Wales and established what might be termed the thirteen historic counties of Wales, that is;
In general when considering the question of British counties, it is important to distinguish between the above as geographical entities and as political or administrative entities, since the principal towns in each shire were likely to be county boroughs and therefore independent of the administrative entity that was the 'county council'. As far as Wales was concerned, this only applied to Glamorganshire where the towns of Cardiff, Merthyr Tydfil and Swansea enjoyed county borough status and Monmouthshire where Newport was similarly blessed.
From 1974 to 1996
As a consequence of the Local Government Act 1972, on April 1st 1974 the thirteen historic counties were abolished and Wales was divided up into eight regions or upper-tier counties which listed below with their essential pre-1974 equivalent.
This administrative reorganisation resurrected the names of the ancient Welsh kingdoms of Dyfed, Gwynedd, Powys and Gwent, named Clwyd after the principal river that flowed through the area and divided Glamorganshire (the most industrialised and populous of the former thirteen counties) into three.
This arrangement lasted for twelve years and all though they have since disappeared as political units, they still have some relevance as Schedule 1 Part III of the Local Government (Wales) Act 1994 defines these (with some minor territorial realignments) as the Preserved Counties of Wales. The counties are 'preserved' because they are still used for the purposes of dividing Wales into United Kingdom parliamentary and Welsh Assembly constituencies, and for determining the areas for the commission of the peace and the offices of sheriff and lieutenant.
From 1996 to date
As a result of the Local Government (Wales) Act 1994 on April 1st 1996 the previous eight counties (together with the thirty seven second tier district councils beneath them) were abolished and replaced with twenty two new 'Unitary Authorities'.
Schedule 1 Part I of the Act lists the eleven that are counties;
and Schedule 1 Part II of the Act lists the eleven that are county boroughs
The distinction between the eleven that are counties and the eleven that are county boroughs is entirely academic; the Act created twenty two authorities and gave them the option of deciding how they should be named. Connurbations such as Newport and Wrexham opted for county borough status, but Swansea and Cardiff prefered to be known as counties and style themselves as 'City and County of'.
It should also be understood that whereas Pembrokeshire, Carmarthenshire, Anglesey and Cardiganshire are almost exactly identical to the original historic counties that bore those names; the geographic areas represented by Denbighshire, Flintshire and Monmouthshire are quite different from those of the historic county.
Sourced from the GENUKI website and the National Gazetteer of Wales at http://www.gazetteer-wales.co.uk together with the the text of the Local Government (Wales) Act 1994.