OutLines

We need to clarify a few things before answering, because you are describing more than a simple circle here.

David M. Camp said:

If I was to have a circle drawn with a "line" and this line is "4pt" in width.

If I assume it was drawn in Coreldraw rather than imported from somewhere else, then the 4pt line will consist of 2pt inside the circle and 2pt outside the circumference of the circle :

But ,,, if you fill the circle -- then you have two choices. You can choose the outline to be in front or behind your fill.

The default is for the outline to be in front in which case the whole 4pt is visible but some of your fill is hidden, so that it seems to be 4pt smaller than it was drawn :

But there is an option in the outline pen properties (F12) to put the outline behind the fill, in which case you see all of the fill but it hides half of the outline.

David M. Camp said:

Now if I put an "Outline" around this circle with another "4pt" line,

This is the bit I need to ask, because there are several possible ways of doing that.

1. Convert the outline of your circle to an object, or
2. Create a contour.
3. Draw a second circle for the new outline (in which case the answer depends entirely on how big you choose to make the second circle).

I think you are probably doing no 1 here. In that case, your "old" outline becomes a fill and can accept a new outline.

If that new outline is 4pt and is set to be behind the first outline (the green area, which is now a fill), then 2pt of it (shown in blue) will be visible on both sides of the green, inside and out

But if that new outline is in front of it, then it will entirely hide the original outline, so you will see what looks like a single 8 point outline ...