Down the block/around the corner

Hello there;
what does down the block mean?
The supermarket is downthe block
and I wonder if “around the corner” has anything to do with ‘the corner of the street’ or it only means nearby and doesn’t necessarily mean on the corner of a street.
Thank you all;

down the block = along the course of the block: apart from where you are standing along the block.
around the corner = at the periphery of the corner.