What is the difference between F+ (closure of F) and F* (cover of F) for Functional Dependencies?
Closure and cover are two completely different things. 

The closure of a set of attributes or a functional dependency $f$ is a set of relation schemes that can be implied by $f$. In order to find the closure, we can expand the FD or the set of attributes based on the given set of FDs by replacing each relation with the ones inferred by it. For example,

$$X = \{ f_1:A \rightarrow BC,~~~ f_2: C \rightarrow D,~~~ f_3: BD \rightarrow E, ~~~~f_4: F \rightarrow G , ~~~~f_5: F \rightarrow H \}$$

then the closure of $f_1: A \rightarrow BC$ or $\{A\}$ is $\{A,B,C,D,E\}$:

$$A \rightarrow_{f_1} ABC \rightarrow_{f_2} ABCD \rightarrow_{f_3} ABCDE$$

while the closure of $F\rightarrow G$ is $\{F, G, H\}$.

The cover of a set of functional dependencies $X$ is a set of functional dependencies $Y$ that is equivalent to $X$ and the left-side of each functional dependency in $Y$ is unique. Though, not every cover is minimal, and we are usually looking for minimal cover. For example a cover of $X$ is,

$$Y=\{f_1:A \rightarrow BC,~~~ f_2: C \rightarrow D,~~~ f_3: BD \rightarrow E, ~~~~f_4: F \rightarrow GH \}$$

Please do some search before posting your questions, there are plenty of resources on the web, including Wikipedia and Wikipedia.