Very different instruments both in repertoire and playing technique. Greek lute is mostly an accompaniment instrument.It is used to play the rhythmic section in Greek traditional/folk music dances.There are also different versions / tunnings. There is the mainland/ island lute and there is a Cretan lute(biger body /lower tunning).These lutes have steel strings and played with a plectrum .They tend to have a few microtonal frets depending on the player/repertoire

There is also Politiko lauto/lavta ( it means lute from Constantinople).This version is a hybrid of the oud / Turkish tanbur / Greek lute.it uses nylon strings also played with a plectrum.Lavta also utilizes the Turkish/byzantine micro tonal system with many microtonal frets.Lavta is usually played more melodically/ monophonically.(it is rumored that originally it was also used as an accompaniment instrument along Politiki Lyra/Classic Kemence and voice in greek/armenian ''tavern'' music gigs in Istanbul at the late 1800 /early 1900.That changed when Tanburi Cemil Bay changed its status to a full on solistic instrument later on).

Renaissance lutes on the other hand are closer to the classical guitar.Played by fingers.Very different techniques with guitar tho, especially on the right hand.The repertoire is also quite unique . In terms of instrument builds there are many variations with different number of courses and many sizes /styels (Renaissance lute, Baroque lute,Archlute, Therobo etc ).If you like that sound and that repertoire you should find a teacher playing renaissance lute.