The Koch Curve is created by using a seed shape to replace each straight line in the figure, which is a line. This seed shape is also referred to as the first generation, but I think to envision it as a seed makes its function clearer. You plant a seed and it grows. That is how it works with a fractal.
The Koch Snowflake uses the same seed shape as the Koch Curve. It is two sides of a triangle in the center of a straight line of which it is a third.
Instead of beginning with a straight line one begins with an equilateral triangle. Each side of the triangle is replaced with the seed shape, two sides of a triangle in the center of a straight line or which it is a third. Then each line segment of the snowflake is replaced with the seed shape.