Part and portion
Towards more picturesque speech™
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Part
/pɑːt/ (n.)
An amount or section which, when combined with others, makes up the whole of something. Portion
/ˈpɔːʃᵊn/ (n.)
A part of a whole.
Well, they are exact synonyms. Thereby, we should prefer part to portion because it is shorter and simpler. “Portion” probably exists to suit lawyers, who have a keening, er, ceteris paribus, for synonyms that sound longer and more complicated. And when synonyms are concerned, by definition all else is equal.
A portion feels some what more like a unitary subdivision of a greater massed whole: a portion of fries; a portion of notes, whereas a part is a bit of an indivisible whole: a part of my biscuit; a part of the security package — on this view part is to portion as less is to fewer — but the JC just made it up, so I wouldn’t bet the farm on it.