One type of sampler seems to have started out as a reminder to the stitcher of stitches she might want to use later - so if you came across a stitch you liked you copied it onto your sampler (they were often rolls made up of more and more bits of fabric sewn on as the previous one filled up) and when you needed to stitch something you'd go through your sampler to choose something or refresh your memory about how to do it. They were also used to record patterns or motifs for later use.
Another type is the "teaching" sampler, generally rectangular with alphabets, sometimes pictorial elements, sometimes cross ttch only but loads with other stitches as well - they were used to teach little girls their stitches, and also served as a way of demonstrating how good you were at stitching. At an exhibition I once saw two done by a pair of sisters in the 18th century, worked on 60ct linen - impressive, and they were very neat too!
I don't know why Ukraine has no tradition of them - it can't be that none survive, surely. Perhaps all Ukrainians are just born perfect stitchers with perfect stitch memories so they don't need them

!
PS in Dutch samplers are known as "merklappen" - "marking cloths" because they contained the alphabets for marking bedlinen etc with.