Don't be fooled. The top shape looks like it might be 2-D, but it's 1-D. And the bottom shape is 2-D, not 1-D.
At first glance, some shapes look like 2-D shapes but are really 1-D shapes. And vice versa. To avoid any confusion, always select the shape, and Visio will tell you what type it is.
For example, the arrow shape at the top of this illustration appears to be two dimensional because it has thickness. But if you selected it, you would see its beginning point and its ending point, so it is 1-D for sure. Instead of just representing a concept or an object, this arrow is used to connect other shapes.
On the other hand, the curve shape appears to be 1-D. After all, it looks like just a line. But if you selected it, you would see the eight selection handles that tell you, it's 2-D. So this curve represents the concept of a bell-shaped curve of data. On the other hand, this line cannot connect other shapes.
To many people, "1-D" describes a shape with one dimension, and "2-D" describes a shape with two dimensions. These are familiar definitions of 1-D and 2-D. However, as you can see from these examples, Visio's definitions depend on how shapes behave, not on how they look.