Is the M16 that different from the M4?

All other things being equal, the M16 should be more accurate since it has a longer barrel and a solid stock. If you aren't used to shooting with iron sights, there are a number of YouTube videos that can show you the basics. Hopefully, before you shot qualification, they ran you through a zero range. Also, remember that the rear peep sight as an aperture for zero and one to shoot. Many a soldier has failed shooting through the wrong sight. As a hint to pass, it's damn hard to see that 300 meter target through the peep and you don't have to shoot it to pass. Concentrate on shooting all of the closer ones first.
Trigger time makes for a better shooter. It's hard to find an M16 style AR around here, but if you can come up with one, range time will improve your shooting.

If you learned to shoot with a CCO and are now shooting with iron sights that is likely the difference. Ensuring you have good "dope" on your weapon, good check weld on the stock and other fundamentals is important. Zero the sights and then working on adjusting them based upon the distance you are shooting.

The only significant difference in the M4 and the M16 is barrel length. That could impact you at greater distances but not in close (less than 200 yards).

3 years? In what unit you are?.
Your poor performance is most likely because of lack of practice

I only fired the M4 in BCT. Irons vs CCO are very different. I qualified 40/40 with iron sights and only 37/40 with the CCO. I do not know if its because the CCO's we where using have been used and abused so much that even the slight recoil from the carbine could throw it out of zero, of if i just was not comprehending the optic, but i was constantly using Kentucky windage to make my shots with the CCO. irons i was on with every shot, every time. You just have to practice sight picture, breath control, trigger control, and cheek to stock. But bo amount of "tips and tricks" will make up for range time practice! If you cannot afford to spend hundreds on ammo to practice, they have lazer bullets now for dry fire practice. I recommend looking into that. It'll help with sight picture, breath, and trigger control. But again, nothing replaces true range time... as you need to be familiar with recoil and target sight alignment and re-alignment.

Short answer, yes. Different. CCO to iron sights. Barrel length. Collapsing butt stock. Hand guards to the rail system. Did you use that grip attachment? Did you hold it the same? Use the block under the guards or barrel or not at all? More or less sling wrap around?

I strongly urge you speak to your FLL and such and bring up the SARG. Small Arms Readiness Group. Their training and fundamentals during NTC brought me from a 26 up to high 30's. Overall you'll need more range time and weapon familiarity.
Do you have access to the small sized laser ranges? Bore laser sights?
There are a lot of tips for this, just depends what you are doing and what fits best. Message me and I can give you all the details possible that I use every time and I use for coaching others.

M4 is the updated, more improved, less malfunctioning model.

Depends on the day...sometimes you score high ...sometimes low. When I was younger in the 70's..USMC.. all the rifle range scores were fake including the PFT. I looked at my records...and rhought..when did I do that? The ANG did the same thing.