Map or Place?

I am at a place.
I have a map of the place.
I take out the map and spread it on a table.
There is a one-to-one correspondence between points on the map and points on the place.
For example, I can find a point corresponding to north-east corner of the table on the map.
But these two points are distinct.
One is on the place and the other is on the map.

Photograph taken from Richard's Photostream. Thank you.

Question:
If I am marking a point on the map, am I marking a point on the place or a point on the map?
The map is a part of the place.
Or is the place a part of the map?