There are only four different types of tools one would need to cut these shapes: the roughing gouge, spindle gouge, skew chisel and parting tool.
Of course, there are a considerable number of variations on these basic shapes. For instance, the radius of a cove cut might vary depending on the desired profile. To create coves of different depths and widths, the woodturner would likely choose to employ different widths of spindle gouges, as a spindle gouge cannot cut a narrower cove than the width of the tool. A narrow spindle gouge can be used to cut a wide cove (as long as the woodturner has the requisite skill level), but a wide spindle gouge cannot be used to cut a narrow cove (as it simply won't fit into the narrow area).