The bouzouki is a Greek instrument developed from the Turkish baglama or saz, which usually has 7 strings, and many different tunings. The rounded bowl back is constructed similarly to the baglama or saz, but the rest of the instrument was developed in conjunction with Italian immigrant mandolin makers, who had moved to Greece. The trichordo bouzouki has 6 strings arranged in three pairs, and tuned DAD. The highest D strings are tuned in unison, as are the A strings, whilst the "low" D consists of a pair of strings tuned an octave apart. This effectively means that there are no less than 3 D strings all at the same pitch, and allows for prolific use of open strings played as drones. Unsurprisingly a lot of material for trichordo bouzouki was written in the key of D.
Regardless of any other historic variations of the instrument, the trichordo bouzouki came to Greece from Asia Minor (Turkey) during the enforced population exchange between the two countries in 1923. It may surprise some to realise that the Greek Bouzouki is played in the Anatolian area of Turkey, presumably by modern day Turks with Greek ancestry. I'll not go into why that happened during the population exchange as it would take too long here.
The bouzouki became particular popular in the Athens area, where a new style of music called rebetika began to take shape, something like a Greek blues. This style was heavy into rants about the political situation of the times, and the songs tended to be rather melancholy.
About 1954, Manolis Chiotis, a bouzouki player who had turned to guitar in order to play the American jazz/swing styles spreading across Europe, hit on the idea of a 4 course bouzouki (tetrachordo), and reckoned if it was tuned identically to the top 8 strings of a standard 12 string guitar (CFAD), then it would be easy for guitar players to understand and play, whilst still sounding like the trichordo, as most bouzouki solos are played on the top 2 courses of strings
Chiotis and various others then began to play some swing type tunes on the tetrachordo, often for pure novelty value, much to the consternation of the traditionalists who felt he had bastardised the bouzouki.
Regardless of what opinions prevail, the 8 string tetrachordo is now by far the most popular of the two. There are other variations of the trichordo such as the tzouras, baglamas, and half-bouzouki, but these instruments tend only to be played by specialists.
Bouzouki is not an easy instrument to play, and I doubt whether I'll ever manage more than a handful of the easier tunes. However, it has a captivating haunting sound, especially when played by somebody who knows all of the mid eastern scales.
Despite being about 80% Irish myself, I've absolutely no idea how or where the Irish bouzouki sprang from. All I know about it is that it has a flat back, is tuned however the player wishes, and can be bought for less than half of a Greek bouzouki.
My bouzouki knowledge improves every time I go and visit my sister, but as it's not really a Cretan instrument, the locals say it is used to make Greek music, inferring that Greece is foreign to them.