A "Fan" in Int'l style is two different things: (1) A dance position, and (2) a syllabus figure.
"Fan" as a dance position is as follows: Man and lady stand apart at right angles to each other, with the lady on the man's left side. (If he were facing the line of dance, for example, then she'd be facing the wall). He holds her right hand with his left.
There's a better description, along with an illustration, in the BDC learning center. Here is a link to the page:
Fan Position.
In American style there really isn't anything comparable to the Fan
position, (although in the old Arthur Murray syllabus they did once include a variation called "L to inside turn", which was essentially a Fan, but that has since disappeared). The Fan position is, in fact, one of the main defining elements of Int'l style, such that if you were to dance a Fan with someone socially, they would almost automatically assume that you are not dancing American style.
Now there is, of course, the Open Break in American style, which gets the same job done. Anything you do in Int'l style with the Fan can be done in American style with the Open Break. For example, a "Fan to Alemana" translates to an "Open Break & Underarm Turn to R", more or less.
The main difference between the two is the man's position to the lady: With an open break, he is facing her directly, whereas with the Fan, he is turned a quarter turn to the right. This positioning affects whether she will rock back, as in the Open Break, or close her feet, as in Fan (the syllabus figure).
Regards,
Jonathan Atkinson
www.ballroomdancers.com