Source entropy and other questions related to information theory
If you look at wikipedia you see that topological entropy is modeled after Kolmogorov-Sinai (KS) entropy, but it is defined without reference to a probability measure $\mu$ on the space. 

For KS entropy, you need to use Shannon entropy: $-\sum_i\mu(X_i) \log \mu(X_i)$ for some partition of the space $\{X_i\}$, which can only be defined if you have some probability measure $\mu$ on your space, while topological entropy is defined without reference to a probability measure. 

Since putting different probability measures on the space will give different KS entropies, while not affecting the topological entropy, these entropies are different. However, they are related by the theorem that the topological entropy is the supremum of the Kolmogorov-Sinai entropy over all probability measures $\mu$.