Unity transform.Translate changed object directions not as expected
Translate by default uses local space!
It sounds like your object (or some parent in the hierarchy) is rotated by 90°.
If you wanted global axis you should rather use
transform.Translate(movment * Time.deltaTime * speed, Space.World);
or to simplify your second snippet you can also do
transform.position += movment * Time.deltaTime * speed;