Yes a FIM is a flight interruption manifest. It is a document...kind of looks like a hand-written carbon copy ticket type thing. It is a way for one airline to issue you a ticket on another. The airline that is "fiming you" will pay the carrier you are going on some discounted amount for your ticket. I think its like 25% or so of the full Y fare that the other airline pays the carrier taking you...but not 100% sure each airline may have its own arrangements. In lieu of writing you a fim, an agent might instead just book you on another carrier, and write on your flight coupon(s)
"rule 240 endorsed to xx"
where XX is the airline they are sending you too.

Writing a fim is the more official and formal way to do it...and just writing on your ticket is the quick informal way of doing it. I don't know exactly what determines when either method will be used.