A stiff putty knife and a flexible putty knife differ primarily in their blade rigidity and intended use. 
A stiff putty knife has a rigid blade, usually made of thicker, harder metal. This rigidity makes it ideal for tasks requiring force and precision, such as scraping off old paint, removing wallpaper, or prying up materials. The stiff blade provides leverage and control, allowing the user to apply pressure without the blade bending. This type of knife is also useful for spreading thick materials like epoxy or cement where a firm application is necessary.
In contrast, a flexible putty knife features a thinner, more pliable blade. This flexibility is advantageous for tasks that require a delicate touch, such as spreading soft materials like spackle, joint compound, or caulk. The flexible blade allows for smooth, even application over surfaces, minimizing the risk of gouging or leaving streaks. It is particularly useful for filling small holes or cracks, as it can conform to the surface contours, ensuring a seamless finish.
In summary, the choice between a stiff and flexible putty knife depends on the specific task at hand. A stiff putty knife is better suited for heavy-duty scraping and prying, while a flexible putty knife excels in spreading and finishing applications.