Vincent,
I started to answer this and soon realized that it was going to be complicated.
The structural element of a building is usually considered a post…as in ‘post and beam construction’, but not always.
Pole barn…. a barn that is constructed with support poles that serve as the underlying support structure for the outer walls and roof.
I copied this from the Unabridged Oxford for you.
1) POST… A stout piece of timber, or other solid material, of considerable length, and usually of CYLINDRICAL or SQUARE shape, used in a vertical position, esp. in building as a SUPPORT FOR A SUPERSTRUCTURE.
A post can be a pole.
2) POST…A stout stick or stake, usually of wood, with a pointed end for driving into the ground, stout POLE, column, or the like, that is set upright in or on the ground, for various purposes; e.g. as a boundary mark, landmark, or monument, a stand for displaying public notices, a support for a fence, a point of attachment, etc.
POLE…
In modern use a long, slender, and more or less CYLINDRICAL and tapering piece of wood (sometimes metal), as the straight stem of a slender tree stripped of its branches; used as a SUPPORT for a tent, hops or other climbing plants, telegraph or telephone wires, etc., for scaffolding, and for other purposes.
Telephone pole
Mast pole
Goalpost
pole vault
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when they both mean "a stick"?
Pole used to have a more general meaning which included 2) POST. This older meaning is still retained in many informal uses (with or without a pointed end) where pole and post are interchangeable.
POLE… In early use, a strong stick or POST, usually of wood, with a pointed end for driving into the ground; used e.g. to mark a boundary or site, to support a plant, to secure an animal, to form one of the component parts of a fence, hedge, or the like, WITHOUT REFERENCE TO LENGTH OR THICKNESS. The modern sense becomes clear first c 1440.