Why there is 2 type of equation for plane progressive wave?

Progressive wave is a type of transverse wave . which can propagate easily in string where y (x, t) is displacement 
a is amplitude 
w is angular frequency or velocity
k is phase constant 
@ initial phase 
A wave which travels continuously in a medium in the same direction without any change in its amplitude is called aprogressive wave or a traveling wave. Aprogressive wave may be transverse or longitudinal in nature.Suppose that a planesimple harmonic wave travels from origin O along the positive direction of X-axis

The equation for progressive wave is=kx-ωt={2π/(Lambda)}(x-vt).