Two differences. Firstly, the extent of reaction $\xi$ can be mathematically defined, whereas the "position of equilibrium" is for the most part qualitative, in the sense that we only say it "moves left" or "moves right", but not "the position of equilibrium is $x$".
More importantly, the extent of reaction does not actually tell you anything about the equilibrium. In this respect, it is more analogous to the reaction quotient $Q$ rather than the equilibrium constant $K$. If you measure the extent of reaction $\xi$ when the system is at equilibrium, then it does provide a measure of the equilibrium position. This is just like how if you measure $Q$ at equilibrium, it is equal to $K$. However, in principle you can measure $\xi$ (or $Q$) at any stage of the reaction, not just when it is at equilibrium.
Both $\xi$ and $Q$ are mathematical ways of describing how much products there are versus how much reactants, but they are not equivalent, they have different forms. See Wikipedia for more information.
So, I don't agree with the statement that "the extent of reaction is indicated by the value of the equilibrium constant" on two counts. Firstly, the extent of reaction is not directly "indicated" by $Q$ – they both measure the same thing, but not in the same way. Secondly, and crucially, $Q$ is not the equilibrium constant $K$: it is only equal to $K$ at equilibrium, which this sentence doesn't capture.