Streak is the color it makes when two minerals scratch against each other. Hardness is just how hard the mineral is
The physical property used to differentiate between pyrite and gold is their hardness. Gold is relatively soft and can be easily scratched, while pyrite is harder and more resistant to scratching. This difference in hardness can help in distinguishing between the two minerals.
The four properties of minerals are color, streak, hardness, and luster. Color refers to the outward appearance, streak is the color of a mineral when it's powdered, hardness is the resistance to scratching, and luster describes the way light reflects off the surface of a mineral.
The color of pencil lead streak is usually gray or black, depending on the hardness of the lead. The softer the lead, the darker the streak it creates.
Topaz is a hard mineral, ranking 8 on the Mohs scale of hardness, so it is harder than most common materials used to test streak. Since streak tests are typically performed on softer minerals, such as using a porcelain streak plate with a hardness of about 6.5, the topaz does not leave a streak because it is harder than the material being used for the test.
Hardness measures a material's ability to resist permanent deformation, whereas brittleness measures a material's tendency to fail or break without undergoing significant deformation. In other words, hardness relates to the resistance to scratching or indentation, while brittleness relates to the tendency to fracture.