Normalization usually means min-max scaling: subtract the minimum, divide by the range, landing every value between 0 and 1. Standardization subtracts the mean and divides by the standard deviation, giving mean 0 and spread 1 with no fixed bounds.
The practical split is bounds versus distribution. Min-max guarantees a range, which suits pixel values and network inputs that expect one. Standardization guarantees location and spread, which is what linear models and principal component analysis assume.
Neither changes the shape of the distribution. Standardizing a skewed column leaves it skewed; if you wanted symmetry, you need a log or power transform instead.
Min-max is the fragile one. A single extreme maximum squeezes every other value into a narrow band near zero, and the range you fitted on rarely holds for future data.
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