lard = rendered pork fat

leaf lard = (specifically) a fine, soft, white fat rendered from the fat in the kidney region of pigs and hogs

In Praise of Lard, and How to Render Your Own
At its simplest, lard is rendered pork fat. Leaf lard, specifically, is a fine, soft, white fat rendered from the fat in the kidney region of pigs and hogs. It is mild in flavor, soft in texture, and particularly well-suited to pastry making.
https://food52.com/blog/10423-in-praise-of-lard-and-how-to-r...

I had my food-grade buckets all clean and ready to hold the masses of leaf fat I expected to get. Leaf fat is what is found around the kidneys. It is the most mild-tasting fat from an animal, and leaf lard makes excellent pastries and homemade pie crusts.
[...] “When we did render lard, we used EVERY bit of fat on the hog. Back fat, kidney fat, any fat that easily trimmed off the hog. We never just render the leaf, of kidney fat. And on an “average” size hog, there might only be 2 to 4 lbs. of the leaf/kidney fat EVER. The kidney on the hog is not near the amount that is on the beef. But to get any decent amount of lard from a hog, you would have to render ALL the fat possible. On average, if I remember correctly from 20 years ago, a 250 lb. on foot hog would get about 20 to 30 lbs. of lard.”
https://www.theprairiehomestead.com/2013/01/the-mystery-of-t...