Wrapping the complexities of alternative algorithms: What is the proper "term" for it?
Hybrid algorithms.

In sorting algorithms it's rather common, Start with quicksort and if the size of the array is small enough switch to insertion sort (much faster for small $n$). Additionally when the recursion depth becomes too large (threatens to become $O(n^2)$) fall back to heapsort (guaranteed $O(n\log n)$).