You did not answer the question. How are they different?
Fast and Frugal heuristics can be descriptive (meaning human beings naturally use them at some level) or prescriptive (here are some good heuristics you can learn to use). Heuristics in Heuristics and Biases are only descriptive.
The Heuristics and Biases theorists would never suggest someone should try to "use" one of their heuristics, nor probably could you even if you tried. You could not intentionally reproduce the pattern of cognitive biases that their heuristics allegedly cause, many appear to be irretrievably outside of conscious awareness ...
This came on the nyc list, I thought I would adapt it here.
Cognitive biases have names. That's what makes them memetic. It's easier to think about something that has a name. Though I think the benefits outweigh the costs, there is also the risk of a little Albert: a concept living on after the original research has been found to be much more ambiguous than first realized.
There are many errors that are possible with respect to named ideas, and despite being studied generally scientifically, cognitive biases are no exception. There is no equivalent to cognitive biases as the Académie Française is to French.
Let's describe some. Here they are: