Analyzing time complexity for change making algorithm (Brute force)

Question

I'm new to analyzing time complexities and I have a question. To compute the nth fibonacci number, the recurrence tree will look like so:

Since the tree can have a maximum height of 'n' and at every step, there are 2 branches, the overall time complexity (brute force) to compute the nth fibonacci number is O(2^n).

Now, looking at the coin make change problem. If the coin denominations are [1, 5, 10, 25] and the input number to make change for is 'C', the recurrence tree should look something like this:

In this case, the tree can have a maximum height of 'C' and the number of branches per step is 4 (The number of coin denominations we are given. Let's call this 'n'). With that being the case, shouldn't the time complexity be O(n^C). I read everywhere that the time complexity is O(C^n). Can someone please explain?