The difference is so fine, I would suggest you don't bother about it. However, as I am a purist, I'll give you my understanding:
for example: used to introduce something chosen as a typical case
"Hilda, for example, is one of the many homeless living on the streets of New York."
With 'for instance':
"With the economic downturn, unemployment is on the rise. In the electronics industry , for instance, 5,000 jobs are being lost."
Here, the electronics industry is not 'a typical case' of some category or class, but just one case where jobs are being lost and unemployment in that area of work is rising