The term contraction can mean:
in metric space theory: see short map
in fixed point theory and topological vector spaces: dilation with coefficient $\lambda\lt 1$
in differential geometry/linear algebra: tensor contraction refers to the evaluation of tensors on each other (such as of differential forms on vector fields).
in formal logic and type theory: the contraction rule is one of the structural rules,
homotopy theory: see at contractible homotopy type
for the corresponding notion in
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