A lot of the comments use special relativity, which means time of someone moving fast is observed differently by the other, but it indeed goes equally fast. It just looks slower.
However, the question did not specify speed, only “space”. The difference there is gravity: almost zero in space, much bigger on earth. This needs general relativity. The higher your gravity, the slower time goes by. So the oscillations in your clock effectively go slower, because of gravity. In this case it’s not just an observed difference, but an actual difference.
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