The difference is capacity and length. A full size aluminium cryocane holds five or six ampoules depending on ampoule diameter. A half cane holds three. On an ordering sheet the two look almost identical, which is why the wrong one gets ordered more often than any other consumable in the chain.

Both are aluminium for the same reason. Aluminium tolerates repeated cycling between room temperature and liquid nitrogen without embrittlement, and it stays light enough to lift one handed out of a canister while wearing cryogenic gloves.

Choose by the geometry of what the cane sits in, not by preference. Half canes suit shallower goblet and canister arrangements, and they make sense where a canister is shared between several sample groups and you want more separations in the same footprint. Full size canes give you fewer canes to handle for the same ampoule count.

One thing to check before ordering either: sleeve length has to match cane length. A full size sleeve on a half cane leaves the top open and defeats the point of sleeving, so order half cryosleeves alongside half canes rather than assuming stock sleeves will fit.