Struggling to make sense of Km
The situation you described is entirely normal. $V_{max}$ is the same, so when described with a graph of initial reaction rate vs. substrate concentration, both curves will asymptotically approach the same maximum level. $K_M$ is higher in one than the other, so the exact shape of the curve as it goes from 0 to $V_{max}$ is different. As you may know, you can interpret $K_M$ as the substrate concentration that causes the initial reaction rate to be half of $V_{max}$. This means the substrate with the higher $K_M$ will have a shallower first half of the curve. 

You can read more about these parameters and initial enzyme kinetics in Berg biochemistry or at khanacademy.