Great picture

heres how I see parts vs alters using your orange picture...

An orange has normal "parts"...

the skin
the segment wall
the pulp inside the segment walls
seeds

each of these parts yes make up the whole orange.

the orange is sitting on the table and rolls off.

one part of that orange gets bruised.

this damaged part of the orange most of the time does not affect the rest of the orange. its safely encased inside one segment/ segment wall

but sometimes because of heat or cold it may affect other parts of the orange like making the near by parts of the orange have a bad taste or odor. but other than that its not a big problem.

same situation in "alters"

the orange rolls off the table each part of the orange has their dissociation symptoms.

(it breaks inside in a way that the bruise is now a separate part of the orange you know how sometimes when you peal an orange theres a part of the orange already broken off from the rest of the orange its not connected to the orange core or the segments next to it.)

the segment that is now free from the rest of the segments starts functioning like its own little orange, the seed grows and as it grows it uses up the fluids in the pulp but remains separate from the rest of the orange.

when the large orange finally gets pealed the person pealing it gets surprised by seeing a little orange inside or a big orange.

(another fruit and veggie you can use this analogy with is bell peppers )