Computational complexity theory (CC) is the study of problems and how to solve them algorithmically. The holy grail of CC is to fully determine the complexity of a problem, that is to answer: How difficult is it to solve this problem? This involves establishing the minimum amout of resources that is necessary and sufficient to solve it. In practice, this is done by giving an algorithm that solves the problem, determine its resource usage, and then prove that there is no algorithm that uses less.

The algorithmic complexity of a problem is its complexity as measured by the worst case runtime of algorithms solving it. Computational complexity theory is however not interested in the ‘complexity’ of algorithms. What would that even mean? Cyclomatic complexity? - It may sound very silly, but I cry a little inside whenever someone talks about the ‘complexity’ of an algorithm when they actually mean the worst case runtime.

And yes, there are plenty of books and academic that will disagree on how this is used, but if words can mean whatever we want them to, why not choose a meaning that actually makes sense?