"An instance" is talking about something real, something that actually happened Example: There are some grammar rules that people don't really pay too much attention to in daily life, for instance, the rules regarding the use of these two phrases. "For example" and "for instance" are often used interchangeably to avoid repetition. "An example" can be talking about something real or something that is theoretical which serves an illustration of something. Example: I love to try new things and take risks, for example, one day I want to go skydiving. Hope this helps!

Most people use them interchangeably, and would have to think about what the difference is. But if you didn't know, using the wrong one might sound weird in some cases. Technically, "for instance" is a more restricted use phrase, used when someone is mentioning a specific example of a general type of thing. I.E. "I have had trouble running more than five miles without hurting my legs, for instance the other day I tried running along the beach, and ended up feeling very sore." "For example" is more general, and is generally used when one is making an example of something. I.E. "I like many sports, for example running and boxing."