Even as someone who's tested recipes professionally and written about food for years, I still always stumble when I'm about to write about a piece of fish — is it fillet or filet? What's the difference? Turns out that it's a bit complicated!
There are similarities between the two words — they're pronounced the same way, for instance: fiˈlā, with a silent "t" on the end. But then it gets a little more interesting.
Fillet is actually both a noun and a verb. Filleting refers to the process of cutting meat or fish off of the bone. While the resulting piece of boneless meat or fish was historically called a fillet, it is now often used only in reference to fish. In other countries, however, the cut of meat known as a chicken tender is referred to as a chicken fillet.
Filet is the alternative French spelling of fillet. The confusing part of it is that filet can also refer to boneless meat or fish. However, its most common usage in the US is for a piece of steak cut from the beef tenderloin or other expensive cut of meat, with the filet mignon being a steak cut from the thickest part of the tenderloin. Because of this usage, filet is used more widely in reference to meat than fish.
So while the general practice now is to refer to fish in fillets and meat in filets, you'd really be making no error if you do the opposite!