My wife bought these 2 cuttings from a nursery in Greece 5 years ago, but we have no idea what variety they are, and really hoping someone can help us identify them.
Also, secondarily looking for any advice on trying to get them to fruit and when to move in-ground

DETAILS:
Size at planting: 18-inch cuttings, no leaves
Age:  5 years old
Current tree size:  4' H x 3' W (when they have all leaves)
Pot size: Years 1-3 in a small 1x1 pot, Years 3-5 a black pot, 2' W x 1.5' H
Fertilized: Not when first planted, but in year 3 when moving to larger pot I used 50% native 50% miracle gro potting for trees. Have not fertilized at all since
Watering: Spring/Fall - every 3 days, but only if it doesn't rain (see note below)
Sun: Year 1-3 sat on east wall of house, brought indoors every winter. Year 3-5, moved to a west wall and get about 10 hours sun in summer
Fruit:  Year 1-3 nothing, Year 4 - each produced about 5 figlets, but never reached ripening, Year 5 (current) - nothing, not even buds

The first 3 years in small pots, they always produced a lot of leaves, but never grew at all.  They literally exploded when I moved them to the larger pots.  The new pots have those reservoirs at the bottom that store water for extended periods... not sure if that's good/bad, but that's primarily why I don't water them daily.  In hotter summer months I try to water every other day, esp if I see the reservoir is empty.  I plan to move these to in-ground this fall or maybe spring?

The first 2 pics are of 1 of my 2 trees (in pot), and the last 2 are from a fully mature tree in Greece (it's probably over 30 years old and is about 20-25 feet tall and 30 feet wide).

Just a guess, Kadota Fig, one of my favorites. A very sweet fig.

Thanks... that's certainly possible.  What about Peter's Honey?
Here is another pic with a better close up of the fruit

   

What color are the figs,skin when fully ripe

Oh and one more thing I just remembered was that this variety has a drop of honey-like sap that forms on the eye when ripe (not all of them, but most).  The fruit is very, very sweet tasting (on the order of Black Mission).  I have tried Kadota's from the farmer's market before, and these are much sweeter than those from what I recall...

I wouldn't try to plant anything in ground unless you have a back-up plant that will stay in a pot.  Even in Z 8 a lot of figs plants will die to the ground in the winter and not produce fruit the following summer.

Ok here are pics of fully ripe figs from the parent tree... it looks like the ripe ones are yellow, but I awaiting confirmation.
Also I was told this tree is over 50 years old (could be 100), and is currently about 20 feet high and 30 feet wide

 

I saw it mentioned in the original post that this was bough at a nursery in Greece,might be worthwhile considering Greek varieties?,I know there is a seller on the UK eBay site selling Greek figs(I believe they were imported from Cyprus),might be worthwhile going on eBay.co.uk and searching Greek Fig,there are quite a few varieties,not all have pics of the fruit but do have pics of the leaves.Im sure that there should be info on Greek figs here in the forum too if you use the search function

Thanks for the tips!  I did search ebay.uk through many listings of greek figs, with no luck matching it (yet).  Still searching through many pages of threads here on figs4fun as well... there are hundreds to read through, lol... but I love it... learning so much out here!  :-)