Square $CASH$ and regular pentagon $MONEY$ are both inscribed in a circle. Given that they do not share a vertex, how many intersections do these two polygons have?
1. **Understanding the problem**: We have a square $CASH$ and a regular pentagon $MONEY$ inscribed in the same circle. We need to determine the number of intersections between these two polygons.

2. **Analyzing the intersection points**: Each side of the square intersects with the sides of the pentagon. Since the square and pentagon do not share any vertices, each side of the square will intersect with the sides of the pentagon.

3. **Counting intersections per side**: 
   - A square has 4 sides.
   - A regular pentagon has 5 sides.
   - Each side of the square intersects with each side of the pentagon exactly once.

4. **Calculating total intersections**:
   - Each side of the square intersects with 2 sides of the pentagon (since the pentagon has 5 sides and the square has 4 sides, each side of the square intersects with 2 sides of the pentagon).
   - Therefore, each side of the square intersects with 2 sides of the pentagon, resulting in $4 \times 2 = 8$ intersections.

Conclusion:
\[
\boxed{8}
\]