Hi Rhonda! I wrote that workout so maybe I can help. The weird names are just ones I invented that made sense to me. I'm embarrassed to say that they undoubtedly have official names that I never bothered to find out.
The lying leg press/leg lift combo is just something I came up with to combine two exercises into one. You lie on your back on a mat with your legs straight and a band looped around the bottom of one foot. First you do a set of leg presses by raising your leg up to a 45 degree angle and bending your knee and doing leg presses against the resistance band, just like if you were on a leg press machine. Then you immediately do a set of straight leg leg raises with the band still looped around the bottom of your foot. Then do the same with the other leg, rest, and repeat the superset.
The inner/outer thigh/butt kick combo is also a superset. While you're standing, loop the band around your ankle and the other end around something strong and stationary, like a table leg. Inner thighs are an adductor movement, so you cross your foot with band over your other leg, moving from the outside in to the center of your body. For the outer thigh, you turn around with the band still on your ankle and do an abductor movement, starting with your leg in the center of your body and pressing outward. For the third movement, the butt kick, you face the table or wherever you looped the band and raise your leg straight back as far as you can (it's not really a kick but you see them called donkey kicks or butt kicks).
I know a picture is worth a thousand words so let me see if I can find something helpful.