Ive noticed that in loading screens, you can clearly see how some armor types like metal and leather armor have more pieces to them, like shoulder pieces for the metal arm armors and a whole chest section for the synth chest piece, is this just me or is there some way to have the pieces show up on the character.

Armour in Fallout 4 is made of individual pieces. However they fit with only some types of dress. You can't put them on any dress you find. Vault suit works, as do military fatigues. Most raider dress works as well. There are some dresses which have damage resistance so they can be considered as armour. Most of them however can not be combined with individual armour pieces. Like the one you find on dead bandit outside Sanctuary.

I know that much, i mean take for example the metal right arm piece, for the player character its just the elbow and wrist armor, but in loading screens you can see that it includes armoring for the shoulder, yet that armoring never appears when wearing the armor piece. for the synth chest piece armor, when the character wears it, its just this ring around the neck, yet in loading screens it is shown to have full armoring for the front chest.

I've noticed it as well and it's a bummer...id rather have some clipping issues of whatever and have the armor showing.