I checked out the easy quick trim die on you tube. From What I ca figure out he needs the cutter that goes inside the die. What I can't figure is what holds the case in place during trimming.
Are you talking about one like this: It needs both parts. I am like you, mine fit in a drill or the Lee can be trimmed by hand but that takes a while. I have one like this I use a lot. either by hand or in a drill.My friend came up today and brought a reloading Lee die for his .223. No problem.. As far as as trimming he brought up a Lee Rifle Quick Trim Die. What in the world is this. Never seen one before and a Lyman E-ZEE TRIM. Never seen one of these either. It is a Hand Trimmer Pilot, no thread to screw on a cutter for trimmng like I use on 30/06, 308, 303, 30/30 etc. My trimmer tools I can put in a drill and quickly trim cases and deburr them.
The little Lee tool we both use is all I use now. Forever I did not put it in the drill just did it by hand. Now I have wrist problems and if doing very many the drill is the way to go. I bought a cheap small Walmart battery operated drill that works great. If he is shooting them in an AR they really need trimmed or sooner or later they will hang up. My buddy loaded hundreds and did not bother to trim them. We ended up with about one in 20 that would not chamber so we had to set them aside to shoot in my bolt action. Now, I darn sure trim the 223 reloads. On most straight wall cases I usually do not bother, 38 spec, 38 short ,357 ,44s , 45 colt, 454, and even 45-70. On the 45 acp I load for the revolvers I do not trim and have not had a problem,In your middle picture what I've used in my reloading life except bottom of case is secured in the shell holder and the cutting shaft is inserted into the case mouth and the cutter trims the case. I don't know what the yellow part is in the picture. I use a drill to spin the cutter. The bottom picture I saw on you tube. Our problem is friend has pace maker and can't use an electric drill. Mysef I can walk the dog with a drill. I see what he brought up is missing the part in your bottom picture. When I trim with middle picture I have to use a deburring tool. I always clean inside the throat before resizing. For me this is all I need. I'm teaching him reloading and he's not familiar with all he needs. Its a slow process. Like all of us we didn't learn all this stuff over night.