A time signature isn’t just about beats and measures, it has a stylistic component, where some beats are emphasized more than others. A 2/4 beat is very steady UP down UP down, while 4/4 is UP down up down UP down up down. It also determines where the notes break. A 4/4 piece might have a dotted half note followed by a quarter note, you can make an equivalent rhythm in 2/4, but it would be unusual.
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