What is the difference between the heuristic function and the evaluation function in A*?

The evaluation function, often denoted as $f$, is the function that you use to choose which node to expand during one iteration of A* (i.e. decide which node to take from the frontier, choose the next possible actions, figure out which next nodes those actions lead to, and add those nodes to the frontier). Typically, you expand the node $n$ such that $f(n)$ is the smallest, i.e. $n' = \operatorname{argmin}f(n)$. In the case of informed search algorithms (such as A*), the heuristic function is a component of $f$, which can be written as $f(n) = g(n) + h(n)$, where $h(n)$ is the heuristic function. The heuristic function estimates the cost of the cheapest path from $n$ to the goal. Just for completeness, $g(n)$ is the actual cost from the start node to $n$ (which can be computed exactly during the search). In the case of uninformed search algorithms, you can actually view the evaluation function as just $f(n) = g(n)$, i.e. the heuristic function is always zero.

So, you're right.

For more details, you can take a look at section 3.5 (p. 92) of the book Artificial Intelligence: A Modern Approach (3rd edition), by Norvig and Russell (you can find the pdf online).

What is the difference between the heuristic function and the evaluation function in A*?

The evaluation function, often denoted as $f$, is the function that you use to choose which node to expand during one iteration of A* (i.e. decide which node to take from the frontier, determine the next possible actions and which next nodes those actions lead to, and add those nodes to the frontier). Typically, you expand the node $n$ such that $f(n)$ is the smallest, i.e. $n^* = \operatorname{argmin}f(n)$. 

In the case of informed search algorithms (such as A*), the heuristic function is a component of $f$, which can be written as $f(n) = g(n) + h(n)$, where $h(n)$ is the heuristic function. The heuristic function estimates the cost of the cheapest path from $n$ to the goal. Just for completeness, $g(n)$ is the actual cost from the start node to $n$ (which can be computed exactly during the search). In the case of uninformed search algorithms, you can actually view the evaluation function as just $f(n) = g(n)$, i.e. the heuristic function is always zero.

So, you're right.

For more details, you can take a look at section 3.5 (p. 92) of the book Artificial Intelligence: A Modern Approach (3rd edition), by Norvig and Russell (you can find the pdf online).