'At / from a distance 'means the same , that is , from a place that is not near
From a distance , I cannot make out who he is . He is too far .
Its not fun watching boxing from a distance .
I thought you were Peter from a distance
'In/into the distance 'means at a point ( as in place) far away
On a clear day , you can see the ships sailing in the distance .
You can see Paris from here in the distance .
He just stood there , looking into the distance