I made running headers in ID CS4 Standard. It included a circle. I copied and pasted the circle into PS. I added some graphics into the circle. I then placed the PS file into ID. The circle shrinks on it's own when I do this - I ended up with a circle that was somewhat smaller than the original I started with even though I never touched the size. I tried it several times with diff. graphics and several times that happened but not always. Sometimes the circle maintained it's size. Can anyone explain to me what is going on and how to avoid this?
There's no concept of smart objects between Photoshop and InDesign as you're describing it.
When you copy an InDesign circle to the clipboard, it's a vector object.
When you copy it into Photoshop it becomes pixels at certain dimensions. It could be that Photoshop's antialiasing is slightly changing the dimensions when you save it as an image file.