If a clock measures proper-time interval while moving at constant speed in an inertial frame, that frame measures .
The twin paradox compares proper time along the different world lines of a travelling observer and a stay-at-home observer who reunite. Reciprocal inertial time dilation produces an apparent contradiction only if the traveller's change of inertial frame is ignored.
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One of the best ways to think about it is the transversal time dilation thought experiment.