Both our terms, from the French, have to do with slicing thinly. Well, one of them has more than one meaning depending upon the food being cut. Isn’t that interesting?
Émince is a misunderstood word by most of us home cooks. Sounds like “mince”, doesn’t it? But émincé means to slice very thinly (think paper thin) rather than pulverize. In French, their word for our “mince” is entirely different. This is an example of words that appear to be cognates that are not.
Émincé is more like julienned, but the food is cut shorter than julienned food. Typically, you émincé meats, but the word can also apply to fruits and veggies.
Effilé, on the other hand, can also mean “thinly slice” when referring to, say, almonds or pistachios. I use almonds like that in some of my dishes calling for almond slices (not slivers--slivers are like wedges). Lots of baked goods call for sliced almonds to add crunch. I buy sliced almonds, rather than effilé them--too hard, too dangerous for a clumsy cook like me. Wish I had better knife skills, but there you go!
However, effilé, in a different food context, changes meaning drastically. When referring to haricots (beans), to effilé them is to remove that fibrous string running its length and to snap off the top--sounds like “stringing beans”, doesn’t it. Yep.
Impress folks at your next dinner party by referring to how you effilé-d and émincé-d your way through the food prep! (Before you comment and complain about my French, I know the past tense isn’t as indicated here. Okay?)