mjhjmtu

Say I draw a red image with below code, generate input.pdf:

documentclassstandalone
usepackagetikz
begindocument
begintikzpicture[x=1pt,y=1pt,line width = 1pt,red]
 draw (0,0) rectangle (50,50);
 draw (25,25) circle (25);
endtikzpicture
enddocument

Then include input.pdf and draw the same thing on this image (draw with black):

documentclassstandalone
usepackagetikz
begindocument
begintikzpicture[x=1pt,y=1pt,line width = 1pt]
 node[anchor=south west,inner sep=0,outer sep=0] at (0,0) includegraphicsinput.pdf;
 draw (0,0) rectangle (50,50);
 draw (25,25) circle (25);
endtikzpicture
enddocument

But the black line not over red line perfectly,see below zoomed parts:

What's wrong with my draw on image code?

OK, I just tried what I thought should work, and surprisingly it does. That is.

documentclassstandalone
usepackagetikz
begindocument
begintikzpicture[x=1pt,y=1pt,line width = 1pt]
 node[anchor=south west,inner sep=0,outer sep=0] at (-pgflinewidth/2,-pgflinewidth/2) includegraphicsinput.pdf;
 draw (0,0) rectangle (50,50);
 draw (25,25) circle (25);
endtikzpicture
enddocument

produces

as expected. Why? You put the node with anchor south west, and, as pointed out

by David Purton, your image is wider (and taller) by the line width (since it is wider and taller by half the line width in each direction). And why is this? You draw a path through the specified coordinates, and the line width gets added to this. I know that the explanation is very clumsy, it would be much easier in marmot language, but I am not sure how to type this, so as a compromise I add a figure. ;-)

An alternative to @marmot's solution is to put the image at (25,25) to line up with your circle and anchor it at it's centre:

documentclassstandalone
usepackagetikz
begindocument
begintikzpicture[x=1pt,y=1pt,line width = 1pt]
 node[inner sep=0,outer sep=0] at (25,25) includegraphicsinput.pdf;
 draw (0,0) rectangle (50,50);
 draw (25,25) circle (25);
endtikzpicture
enddocument